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• W2482260433 abstract "This chapter discusses extension problems of real-valued continuous functions. In this discussion, a space means a completely regular T1-space. A subset A of a space X is said to be C-embedded in X if every real-valued continuous function on A extends continuously over X, and A is said to be C*-embedded in X if every bounded real-valued continuous function on A extends continuously over X. Every C*-embedded subset of a first countable space is closed. Kulesza–Levy–Nyikos has proved that if b = s = c, then there exists a maximal almost disjoint family ℛof infinite subsets of ℕ such that every countable set of nonisolated points of the space ℕ Uℛ is C*-embedded. Because every set of nonisolated points of ℕ Uℛ is discrete and ℕ Uℛ is pseudocompact, those countable sets are not C-embedded. This chapter aims to collect some open questions concerning C-, C*-embeddings and extension properties which can be described by extensions of real‑valued continuous functions. Details of π -embedding and π Ƶ -embeddings are also provided." @default.
• W2482260433 created "2016-08-23" @default.
• W2482260433 creator A5083878567 @default.
• W2482260433 creator A5085565188 @default.
• W2482260433 date "2007-01-01" @default.
• W2482260433 modified "2023-09-25" @default.
• W2482260433 title "Extension problems of real-valued continuous functions" @default.
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• W2482260433 doi "https://doi.org/10.1016/b978-044452208-5/50005-3" @default.
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