Metrizable shape and strong shape equivalences
نویسندگان
چکیده
منابع مشابه
Metrizable Shape and Strong Shape Equivalences
In this paper we construct a functor Φ : proTop → proANR which extends Mardešić correspondence that assigns to every metrizable space its canonical ANR-resolution. Such a functor allows one to define the strong shape category of prospaces and, moreover, to define a class of spaces, called strongly fibered, that play for strong shape equivalences the role that ANRspaces play for ordinary shape e...
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If in the classical S-category P, 1) continuous mappings are replaced by compact-open strong shape (= coss) morphisms (cf. §1 or [1], §2), and 2) ∧-products are properly reinterpreted, then an S-duality theorem for arbitrary subsets X ⊂ S (rather than for compact polyhedra) holds (Theorem 2.1). 0. Introduction. In a previous paper [1] we introduced the concept of coss-shape (compact-open strong...
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J. Keesling has shown that for connected spaces X the natural inclusion e : X → βX of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2002
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2002.v4.n1.a6