On cellular-compactness and related properties

Alas, Ofelia T.; Junqueira, Lúcia Renato; Passos, Marcelo D.; Wilson, Richard G.

doi:10.1007/s13398-020-00833-3

Cited by 5 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Bella and Spadaro managed to find such a common generalization by other means (see [5]) but the original question is still open despite several attacks by various authors (see, for example, [2,5,12,14]). Moreover, the introduction of the cellular-Lindel öf property led several authors to study cellular-P-spaces, for various other properties P (see, for example, [1,14]).…”

Section: Introductionmentioning

confidence: 99%

On cellular-countably compact spaces

Singh

2022

Filomat

View full text Add to dashboard Cite

A space X is said to be cellular-countably compact if for each cellular family U in X, there is a countably compact subspace K of X such that U ? K ?? for each U ? U. The class of cellularcountably compact spaces contain the classes of countably compact spaces and cellular-compact spaces and contained in a class of pseudocompact spaces. We give an example of Tychonoff DCCC space which is not cellular-countably compact. By using Erd?s and Rad??s theorem, we establish the cardinal inequalities for cellular-countably compact spaces. We show that the cardinality of a normal cellular-countably compact space with a G?-diagonal is at most c. Finally, we study the topological behavior of cellular-countably compact spaces on subspaces and products.

show abstract

Section: Introductionmentioning

confidence: 99%

On cellular-countably compact spaces

Singh

2022

Filomat

View full text Add to dashboard Cite

show abstract

“…Nessa dissertação conceitos topológicos terão papel central e por isso esse apêndice foi introduzido. Nossas principais referências são [31], [43] e [44].…”

Section: A2 Topologiaunclassified

Estados de equilíbrio na teoria quântica em topoi

Tezzin¹

View full text Add to dashboard Cite

The main purpose of this work was to study equilibrium states in the topos approach to quantum theory. This is a relatively new approach to quantum theory then we also tried to present it in a self-contained way -at least from a mathematical point of view. Concerning equilibrium, we focused on two features: time translation invariance (stationary states) and the KMS condition. We characterize invariant states (in particular stationary states) by means of the so called "measures on the spectral presheaf". We couldn't do the same for the KMS condition and, as argued in this work, we think that there are good reasons to believe that it is not possible.Then, we studied the KMS condition using pseudo-states. For this purpose we introduced the idea of a "topos associated to a state" and proved that in the topos of any state there are at least two propositions (clopen subobjects of the spectral presheaf) which are true (in the sense of the pseudo-state) if, and only if, the state is KMS. One of these propositions is not of the kind "daseinization of a projector" and it can be seen as a way of giving physical meaning to a proposition which is not in the interpretation of the PL(S) language.

show abstract