Matches in SemOpenAlex for { <https://semopenalex.org/work/W2555768235> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2555768235 abstract "This paper develops the Reverse Mathematics of second countable topologies, where the elements of the topological space exist. The notion of topology, eective topology (Dorais 2011), and basis will be dened. Several concepts and results that appear in the practice of general topology will be developed in various subsystems of second order arithmetic, Z2. Several of the ideas and results of point set topology will be proved to be equivalent to subsystems of second arithmetic, primarily ACA0, over the base system RCA0. Various open questions about basic notions from general topologies are interspersed throughtout. Topologies are given by a sequence of sets (Bn)n2N which satisfy all the conditions of being a basis with the additional condition that B0 is the entire topological space. Thus all the topologies considered are such that their points really exist, that is the points are elements of N, and the entire topological space is a set that exists. A set is open if and only if all its points are interior points. It is shown that RCA0 can prove that arbitrary union of basic open sets are open whenever this union exists. However, RCA0 can not prove that arbitrary union of basic open sets exists. It is proved (Theorem 3.12) that over RCA0, ACA0 is equivalent to the existence of the union of basic open sets. Another familiar result from general topology is that a set is open if and only if it is the union of basic open sets. An open code (Dorais 2011) for an open set U is, informally, a set X such that S X Bn = U. A open set that has an open code is called eectively open. It" @default.
- W2555768235 created "2016-11-30" @default.
- W2555768235 creator A5048602275 @default.
- W2555768235 date "2011-01-01" @default.
- W2555768235 modified "2023-09-24" @default.
- W2555768235 title "Reverse Mathematics of Topology" @default.
- W2555768235 cites W1556453281 @default.
- W2555768235 hasPublicationYear "2011" @default.
- W2555768235 type Work @default.
- W2555768235 sameAs 2555768235 @default.
- W2555768235 citedByCount "0" @default.
- W2555768235 crossrefType "journal-article" @default.
- W2555768235 hasAuthorship W2555768235A5048602275 @default.
- W2555768235 hasConcept C110729354 @default.
- W2555768235 hasConcept C111919701 @default.
- W2555768235 hasConcept C114614502 @default.
- W2555768235 hasConcept C118615104 @default.
- W2555768235 hasConcept C123222754 @default.
- W2555768235 hasConcept C129089157 @default.
- W2555768235 hasConcept C129866940 @default.
- W2555768235 hasConcept C134306372 @default.
- W2555768235 hasConcept C143913944 @default.
- W2555768235 hasConcept C148420369 @default.
- W2555768235 hasConcept C164953516 @default.
- W2555768235 hasConcept C166359235 @default.
- W2555768235 hasConcept C176293985 @default.
- W2555768235 hasConcept C177264268 @default.
- W2555768235 hasConcept C184720557 @default.
- W2555768235 hasConcept C199360897 @default.
- W2555768235 hasConcept C199845137 @default.
- W2555768235 hasConcept C2778572836 @default.
- W2555768235 hasConcept C33923547 @default.
- W2555768235 hasConcept C41008148 @default.
- W2555768235 hasConcept C42058472 @default.
- W2555768235 hasConcept C42357961 @default.
- W2555768235 hasConcept C81332173 @default.
- W2555768235 hasConceptScore W2555768235C110729354 @default.
- W2555768235 hasConceptScore W2555768235C111919701 @default.
- W2555768235 hasConceptScore W2555768235C114614502 @default.
- W2555768235 hasConceptScore W2555768235C118615104 @default.
- W2555768235 hasConceptScore W2555768235C123222754 @default.
- W2555768235 hasConceptScore W2555768235C129089157 @default.
- W2555768235 hasConceptScore W2555768235C129866940 @default.
- W2555768235 hasConceptScore W2555768235C134306372 @default.
- W2555768235 hasConceptScore W2555768235C143913944 @default.
- W2555768235 hasConceptScore W2555768235C148420369 @default.
- W2555768235 hasConceptScore W2555768235C164953516 @default.
- W2555768235 hasConceptScore W2555768235C166359235 @default.
- W2555768235 hasConceptScore W2555768235C176293985 @default.
- W2555768235 hasConceptScore W2555768235C177264268 @default.
- W2555768235 hasConceptScore W2555768235C184720557 @default.
- W2555768235 hasConceptScore W2555768235C199360897 @default.
- W2555768235 hasConceptScore W2555768235C199845137 @default.
- W2555768235 hasConceptScore W2555768235C2778572836 @default.
- W2555768235 hasConceptScore W2555768235C33923547 @default.
- W2555768235 hasConceptScore W2555768235C41008148 @default.
- W2555768235 hasConceptScore W2555768235C42058472 @default.
- W2555768235 hasConceptScore W2555768235C42357961 @default.
- W2555768235 hasConceptScore W2555768235C81332173 @default.
- W2555768235 hasLocation W25557682351 @default.
- W2555768235 hasOpenAccess W2555768235 @default.
- W2555768235 hasPrimaryLocation W25557682351 @default.
- W2555768235 hasRelatedWork W132280835 @default.
- W2555768235 hasRelatedWork W1424698467 @default.
- W2555768235 hasRelatedWork W1488039733 @default.
- W2555768235 hasRelatedWork W1548077779 @default.
- W2555768235 hasRelatedWork W1979912753 @default.
- W2555768235 hasRelatedWork W1991083015 @default.
- W2555768235 hasRelatedWork W2036312696 @default.
- W2555768235 hasRelatedWork W2042030906 @default.
- W2555768235 hasRelatedWork W204859252 @default.
- W2555768235 hasRelatedWork W2056474911 @default.
- W2555768235 hasRelatedWork W2072410849 @default.
- W2555768235 hasRelatedWork W2093164193 @default.
- W2555768235 hasRelatedWork W2323366404 @default.
- W2555768235 hasRelatedWork W2332216340 @default.
- W2555768235 hasRelatedWork W2332328989 @default.
- W2555768235 hasRelatedWork W2337431348 @default.
- W2555768235 hasRelatedWork W2519197805 @default.
- W2555768235 hasRelatedWork W2964222779 @default.
- W2555768235 hasRelatedWork W347560160 @default.
- W2555768235 hasRelatedWork W3151833102 @default.
- W2555768235 isParatext "false" @default.
- W2555768235 isRetracted "false" @default.
- W2555768235 magId "2555768235" @default.
- W2555768235 workType "article" @default.