|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4657761||1633066||2016||10 صفحه PDF||سفارش دهید||دانلود رایگان|
We study the internal structure of topological spaces X which can be represented as the union of a finite collection of subspaces belonging to some nice class of spaces. Several closely related structure theorems are established. In particular, they concern the finite unions of subspaces with the weight ≤τ, the finite unions of subspaces with a point-countable base, and the finite unions of metrizable subspaces. As a corollary, we extend to finite unions the classical Mischenko's Theorem on metrizability of compacta with a point-countable base  (see Theorem 11). A few other applications of the structure theorems are given, in particular, to homogeneous spaces ( Corollary 5 and Corollary 10).
Journal: Topology and its Applications - Volume 213, 1 November 2016, Pages 220–229