Memoirs of the Faculty of Science, Shimane University

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Memoirs of the Faculty of Science, Shimane University 23
1989-12-25 発行

距離空間の可算和である層型空間の絶対近傍レトラクト

ANR of σ-Metric Stratifiable Spaces
Guo, Bao-Lin
Miwa, Takuo
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Description
For a real vector space E, the second author introduced the locally convex topology T in [15] such that (E, T) is the strongest locally convex topology contained in the finite topology. In this paper, we shall prove the following.
(1) (E, T) is a σ-metric stratifiable space.
(2) For any σ-metric stratifiable space X, X can be embedded in a AR (σ-metric stratifiable)-space as a closed subset.
(3) For each natural number n, the fundamental subspace E_n of (E , T) is AE(stratifiable).
(4) For any σ-metric stratifiable space X, X is AR(σ-metric stratifiable) (resp. ANR) if and only if X is AE(σ-metric stratifiable) (resp. ANE).