科研之友
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摘要
In this note we show that a T-1 topological space X is a Menger space if and only if for each sequence {phi(n) : n is an element of w} of neighborhood assignments for X, there exists, for each n is an element of w, a finite subset D-n of X such that X = U{phi(n)(d) d is an element of D-n, n is an element of w} and D = U{D-n : n is an element of w} is a closed discrete subspace of X. A T-1 topological space X is a Rothberger space if and only if for each sequence {phi(n) : n is an element of w} of neighborhood assignments for X, there exists, for each n is an element of w, a point d(n) is an element of X such that X = U{phi(n)(d(n)) : n is an element of w} and D = {d(n) : n is an element of w} is a closed discrete subspace of X. Let M be the class of all spaces with the Menger property. Let R be the class of all Rothberger spaces. We show that a M -like space has the Menger property. A R -like space is a Rothberger space. Let C be the class of all compact spaces. Let W be the class of all countable spaces. We prove that a finite product of C -like spaces is a C -like space. As a corollary we know that a finite product of C -like spaces is a Menger space. In the last part of this note we show that a finite product of W -like Hausdorff spaces is a nc-W-like space. A finite product of W -like spaces is a Rothberger space.
- 出版日期2016-2-15
- 单位北京工业大学
