AN APPROXIMATE RESOLUTION OF THE PRODUCT WITH A COMPACT FACTOR

For any given approximate resolution p = {pa|a(EA}: X → X =(Xa, Ua, Paa', A) of a topological space X, where X is uniform, all Xa are paracompact, all Ua are locally finite and A is cofinite, and any given compact Hausdorff space Y, the approximate resolution r= p×1={rb = Pa×1|b=(a, φ)∈B}: X×Y...

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Published in:Tsukuba journal of mathematics 1992-06, Vol.16 (1), p.75-84
Main Authors: Matijevic, Vlasta, Uglesic, Nikica
Format: Article
Language:English
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Hausdorff spaces
Industrial refining
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Uglesic, Nikica
description For any given approximate resolution p = {pa|a(EA}: X → X =(Xa, Ua, Paa', A) of a topological space X, where X is uniform, all Xa are paracompact, all Ua are locally finite and A is cofinite, and any given compact Hausdorff space Y, the approximate resolution r= p×1={rb = Pa×1|b=(a, φ)∈B}: X×Y → X×Y = (Xa×Y, Ua×φ[Va], Paa'×1, B) of the product space X×Y is constructed. Here, the indexing set is obtained by means of the set A and certain subfamilies of Φ(a)={φ|φ:Va→Cov(Y)}, a∈A, while the mesh is Va×φ[va] is a stacked covering of Xa over Va.
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title AN APPROXIMATE RESOLUTION OF THE PRODUCT WITH A COMPACT FACTOR
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