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Samuel compactification and uniform coreflection of nearness σ -frames

Inderasan Naidoo (2006)

Czechoslovak Mathematical Journal

We introduce the structure of a nearness on a σ -frame and construct the coreflection of the category 𝐍 σ F r m of nearness σ -frames to the category 𝐊 R e g σ F r m of compact regular σ -frames. This description of the Samuel compactification of a nearness σ -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform σ -frames in [11]. We also construct the uniform coreflection of a nearness σ -frame, that is, the coreflection of the category of 𝐍 σ F r m to the category...

Seeking a network characterization of Corson compacta

Ziqin Feng (2021)

Commentationes Mathematicae Universitatis Carolinae

We say that a collection 𝒜 of subsets of X has property ( C C ) if there is a set D and point-countable collections 𝒞 of closed subsets of X such that for any A ∈ 𝒜 there is a finite subcollection ℱ of 𝒞 such that A = D ∖ ⋃ ℱ . Then we prove that any compact space is Corson if and only if it has a point- σ - ( C C ) base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in “A Biased View of Topology as a Tool in Functional Analysis” (2014) by...

Selection principles and upper semicontinuous functions

Masami Sakai (2009)

Colloquium Mathematicae

In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and S f i n ( Γ , Ω ) in terms of upper semicontinuous functions

Semiconvex compacta

Oleh R. Nykyforchyn (1997)

Commentationes Mathematicae Universitatis Carolinae

We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...

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