Characterization of precompact shape and homology properties of remainders

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• 作者：Baladze ; Vladimer
• 关键词：Completely regular space ; Uniform space ; Compactification ; Uniform shape ; Uniform resolution ; Cech homology group ; Cech cohomology group ; Cohomological dimension ; Coefficient of cyclicity
• 刊名：Topology and its Applications
• 出版年：2004
• 出版时间：July 28, 2004
• 年：2004
• 卷：142
• 期：1-3
• 页码：181-196
• 全文大小：274 K

文摘

In this paper a precompact shape theory is investigated. Necessary and sufficient conditions are found for which the precompact shapes of remainders are coinsided. An intrinsically characterization of Cech (co)homology groups of remainders is given. Border cohomological dimension, dim_A^∞X, and coefficient of border cyclicity, η_A^∞X, are defined and the inequality dim_A^∞X≤dim_A(cXX) and the equality η_A^∞X=η_A(cXX) are proved for a space X normally adjoined to its remainder.