Components of first-countability and various kinds of pseudoopen mappings

被引：7

作者：

Arhangel'skii, Alexander

机构：

[1] Moscow, h. 33

来源：

TOPOLOGY AND ITS APPLICATIONS | 2011年 / 158卷 / 02期

关键词：

First-countable; Frechet-Urysohn; Countably compact; Pseudoopen mapping; Pseudocompact; Biquotient mapping; S-mapping; Sensor; K-Sensor; Point-countable base; Topological group; Countable fan-tightness;

D O I：

10.1016/j.topol.2010.10.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some new classes of pseudoopen continuous mappings are introduced. Using these, we provide some sufficient conditions for an image of a space under a pseudoopen continuous mapping to be first-countable, or for the mapping to be biquotient. In particular, we show that if a regular pseudocompact space Y is an image of a metric space X under a pseudoopen continuous almost S-mapping, then Y is first-countable. Among our main results are Theorems 2.5, 211, 2.12, 2.13, 2.14. See also Example 2.15, Corollary 2.7, and Theorem 2.18. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：215 / 222

页数：8