Condensations of C-p(X) onto sigma-compact spaces

被引：1

作者：

Tkachuk, V. V. ^{[1
]}

机构：

[1] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, San Rafael Atlixco,186, Iztapalapa 09340, Mexico

来源：

APPLIED GENERAL TOPOLOGY | 2009年 / 10卷 / 01期

关键词：

condensation; continuous image; Lindelof Sigma-space; sigma-compact space; topology of pointwise convergence; network weight; tightness; Lindelof space;

D O I：

10.4995/agt.2009.1786

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show, in particular, that if nw(Nt) <= n for any t is an element of T and C is a dense subspace of the product Pi{Nt : t is an element of T} then, for any continuous (not necessarily surjective) map phi : C -> K of C into a compact space K with t(K) <= k, we have Psi(phi(C)) <= k. This result has several applications in C-p-theory. We prove, among other things, that if K is a non-metrizable Corson compact space then C-p(K) cannot be condensed onto a sigma-compact space. This answers two questions published by Arhangel'skii and Pavlov.

引用

页码：39 / 48

页数：10