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- W2056222078 abstract "Arhangel'skiı̆ defines in [Topology Appl. 70 (1996) 87–99] a subspace Y of a topological space X to be weakly C -embedded in X if for every real-valued continuous function f on Y there exists a real-valued function on X which is an extension of f and continuous at each point of Y . In this paper, we prove that Y is weakly C -embedded in X if and only if for every pair G 0 , G 1 of disjoint cozero-sets of Y there exist disjoint open subsets H 0 and H 1 of X such that G i ⊂H i (i=0,1) . As applications, our characterization gives answers with simple observations to problems posed by Arhangel'skiı̆, which were recently solved by Bella and Yaschenko [Proc. Amer. Math. Soc. 127 (1999) 907–913], Costantini and Marcone [Topology Appl. 103 (2000) 131–153] and Matveev et al. [Topology Appl. 93 (1999) 121–129]. Moreover, suggested by weak C -embedding, we define a notion of weak P -embedding, more precisely, weak P γ -embedding for an infinite cardinal γ , which is an extension of P -embedding. Using this notion we describe weak C -embedding for product spaces with a compact factor." @default.
- W2056222078 created "2016-06-24" @default.
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- W2056222078 date "2002-11-01" @default.
- W2056222078 modified "2023-09-27" @default.
- W2056222078 title "Weak C-embedding and P-embedding, and product spaces" @default.
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- W2056222078 doi "https://doi.org/10.1016/s0166-8641(01)00275-9" @default.
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