Chapter 2 Extensions of Mappings II

Hoshina, Takao

doi:10.1016/s0924-6509(08)70148-x

Cited by 6 publications

(4 citation statements)

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“…Moreover, it is known that 'Banach space' in the above can be replaced by 'Fr\'echet space' (see [2]). A subspace $A$ is said to be well-embedded in $X$ if every zero-set of $X$ disjoint from $A$ can be completely separated from $A$ in $X$ (see [2], [11]). We use the following facts without references; (i)…”

Section: Introductionmentioning

confidence: 99%

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Extending pointwise bounded equicontinuous collections of functions

Yamazaki¹

2005

Tsukuba J. Math.

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Section: Introductionmentioning

confidence: 99%

“…embedded and well-embedded in $X;(iii)X$ is collectionwise normal if and only if every closed subspace $A$ of $X$ is P-embedded in $X$ . For these results, see [2], [11] and [13].…”

Section: Introductionmentioning

confidence: 99%

Extending pointwise bounded equicontinuous collections of functions

Yamazaki¹

2005

Tsukuba J. Math.

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“…Proposition 2]; see Proposition 3.8.) U admits a subordinate locally finite partition of unity;• (Michael[1953, Proposition 1], Hoshina[1989, Theorem 1.1 and 1.2].) U can be refined by an open cover given by the union of a countable collection of discrete families of cozero sets.…”

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confidence: 99%

Numerable open covers and representability of topological stacks

Pavlov

2022

Preprint

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In this note, we establish an analogue of the Brown-Gersten property for numerable open covers of topological spaces: a simplicial presheaf on the site of topological spaces with numerable open covers satisfies the homotopy descent property for all open covers if and only if it satisfies it for covers with two elements and covers with pairwise disjoint elements. We apply this result to deduce a representability criterion for stacks on topological spaces similar to arXiv:1912.10544. We also use this result to establish new simple criteria for chain complexes of sheaves of abelian groups to satisfy the homotopy descent property.

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“…For other basic facts related to -K-analytic spaces, see [9,20]. For extensions of continuous functions, see [1,10]. §3.…”

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confidence: 99%

Products of WeakP‐Spaces andK‐Analytic Spaces

Yamazaki

2007

Mathematika

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Let κ be an infinite cardinal. Okuyama showed that the product space X ×i Y of a paracompact weak P (ω)‐space X and a K‐analytic space Y is paracompact. In this paper, by using the notion of κ‐K‐analytic spaces which is basically defined by Hansell, Jayne and Rogers, the above result is extended and some other results are given related to normality, collectionwise normality and covering properties on products. An answer to a question of Okuyama and Watson is also given, as well as some applications to extensions of continuous functions on these products.

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Chapter 2 Extensions of Mappings II

Cited by 6 publications

References 25 publications

Extending pointwise bounded equicontinuous collections of functions

Extending pointwise bounded equicontinuous collections of functions

Numerable open covers and representability of topological stacks

Products of WeakP‐Spaces andK‐Analytic Spaces

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