standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.| relation to other work | claim_relations | how this paper stands to another: agrees, contradicts, extends, qualifies |
| claim type | claim_type | the shape of the claim: existence, mechanism, method, critique, prediction, null |
| concept edge | concept_edges | an asserted relation between two concepts, with the sentence asserting it |
| concept | concepts | an idea the paper works with, quoted where the paper uses it |
| content tag | content_tags | a finding, definition, quantity, statistic or variable named in the paper |
| limitation | limitations | what the paper says its evidence cannot support |
| mechanism | mechanisms | how the reported effect is said to come about |
| method | method | how the paper produced its evidence |
| phenomenon | phenomenon | the effect or regularity under study |
| sense | senses | a distinct use of a term, quoted where the paper fixes it |
Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 1 relation here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.
This record holds no controls. A layer is empty when the tagger recorded nothing in it — which is not the same as the paper having nothing to record.
| facet | tag | field | conf. | whose words |
|---|---|---|---|---|
| claim_type | existence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_type | the paper's words | |
| phenomenon | de Vries duality for compact Hausdorff spaces Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | phenomenon | the paper's words | |
| method | mathematical-proof Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mathematical-proof | method | the paper's words | |
| mechanisms | mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[0] | the tagger's words | |
| limitations | One of the intermediate categories the construction produces has badly behaved isomorphisms. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[0] | the tagger's words | |
| limitations | In one of the categories used, two objects can be isomorphic while differing in cardinality, so the word does not carry its usual force there. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: a statement that two objects of StoneER are isomorphic: isomorphism there is not a structure-preserving bijection, and two objects may be isomorphic even without sharing the same cardinality | limitations[1] | 1.0 | the tagger's words |
| limitations | The composition operation in the classical dual category is not the usual function composition, which is the drawback the paper exists to remove. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any argument that composes morphisms in de Vries' original dual category DeV: composition there is not usual function composition, whereas in the alternative proposed here it is usual relation composition | limitations[2] | 1.0 | the tagger's words |
| limitations | The direction chosen for the morphisms is declared a matter of taste, with the opposite convention giving a dual statement of the same result. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the direction in which this equivalence is stated: the authors call the choice of direction a matter of taste and note the result can equally be stated as a dual equivalence | limitations[3] | 1.0 | the tagger's words |
| concepts | de Vries algebras Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: de Vries algebras | concepts[0] | the paper's words | |
| concepts | closed relation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: closed relation | concepts[1] | the paper's words | |
| concepts | isomorphism Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: isomorphism | concepts[2] | the paper's words | |
| concepts | structure-preserving bijection Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: structure-preserving bijection | concepts[3] | the paper's words | |
| concepts | subordination relations Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: subordination relations | concepts[4] | the paper's words | |
| senses | isomorphism - IN StoneER, NOT A BIJECTION: two objects may be isomorphic even when their underlying spaces differ in cardinality, so the word here does not imply the structure-preserving correspondence a reader would assume Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[0] | 1.0 | the tagger's words |
| senses | isomorphism - IN DeVS AND GleR, RECOVERED: the paper proves that in these two categories isomorphisms ARE structure-preserving bijections, which is what makes them the better home for the duality Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[1] | 1.0 | the tagger's words |
| senses | composition - THE ORDINARY OPERATION OR NOT: in de Vries' original category it is not usual function composition; in the approach proposed here it is usual relation composition, and that difference is given as the advantage Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[2] | 1.0 | the tagger's words |
| claim_relations | extends → de Vries duality [12] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[0] | the tagger's words | |
| claim_relations | extends → the open problem raised in [5, Rem. 3.14] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[1] | the tagger's words | |
| claim_relations | builds-on → Celani [11]'s quasi-semi-homomorphisms and the subordination relations of [4] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[2] | the tagger's words | |
| concept_edges | isomorphism —distinct-from→ structure-preserving bijection Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: isomorphism · structure-preserving bijection | concept_edges[0] | the tagger's words | |
| content_tags | Stone duality lifts to an equivalence between Stone spaces with closed relations and boolean algebras with subordination relations. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[0] | the tagger's words | |
| content_tags | Splitting the equivalences (closed equivalence relations) in the allegory of Stone spaces and closed relations produces a category equivalent to compact Hausdorff spaces with closed relations. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[1] | the tagger's words | |
| content_tags | Splitting the equivalences on the algebraic side produces a category equivalent to de Vries algebras with compatible subordination relations. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[2] | the tagger's words | |
| content_tags | Compact Hausdorff spaces with closed relations are equivalent to de Vries algebras with compatible subordinations, resolving a problem recently raised in the literature. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[3] | the tagger's words | |
| content_tags | That equivalence restricts to one between compact Hausdorff spaces with continuous maps and the wide subcategory DeVF of de Vries algebras whose morphisms satisfy additional conditions. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[4] | the tagger's words | |
| content_tags | One advantage is that composition of morphisms is ordinary relation composition. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[5] | the tagger's words | |
| content_tags | The equivalence is realised concretely by sending a closed relation R to the subordination on regular opens defined by U S V exactly when R maps the closure of U inside V. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[6] | the tagger's words | |
| content_tags | Isomorphisms in the intermediate categories are badly behaved: two S5-subordination spaces can be isomorphic in StoneER while their underlying Stone spaces differ in cardinality. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[7] | the tagger's words | |
| content_tags | In the de Vries algebra category DeVS, by contrast, every isomorphism is a structure-preserving bijection. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[8] | the tagger's words | |
| content_tags | DeVF is dually isomorphic to the classical category DeV of de Vries algebras and de Vries morphisms. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[9] | the tagger's words | |
| content_tags | The construction yields, as a by-product, a new proof that the category of compact Hausdorff spaces is the exact completion of the category of Stone spaces. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[10] | the tagger's words | |
| content_tags | closed relation between Stone spaces Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: closed relation between Stone spaces | content_tags.definitions[0] | the tagger's words | |
| content_tags | quasi-semi-homomorphism Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: quasi-semi-homomorphism | content_tags.definitions[1] | the tagger's words | |
| content_tags | subordination relation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: subordination relation | content_tags.definitions[2] | the tagger's words | |
| content_tags | allegory Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: allegory | content_tags.definitions[3] | the tagger's words | |
| content_tags | S5-subordination Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: S5-subordination | content_tags.definitions[4] | the tagger's words | |
| content_tags | S5-subordination space Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: S5-subordination space | content_tags.definitions[5] | the tagger's words | |
| content_tags | extremally disconnected Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: extremally disconnected | content_tags.definitions[6] | the tagger's words | |
| content_tags | Gleason space Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Gleason space | content_tags.definitions[7] | the tagger's words | |
| content_tags | de Vries algebra Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: de Vries algebra | content_tags.definitions[8] | the tagger's words |
Tags that could not be placed in the text:
What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.