Affiliation:
1. Department of Mathematics, Ningde Normal University, Ningde, Fujian, P.R. China
Abstract
Let I be an ideal on N. A mapping f : X ? Y is called an I-covering mapping
provided a sequence {yn}n?N is I-converging to a point y in Y, there is a
sequence {xn}n?N converging to a point x in X such that x ? f ?1(y) and each
xn ? f ?1(yn). In this paper we study the spaces with certain I-cs-networks
and investigate the characterization of the images of metric spaces under
certain I-covering mappings, which prompts us to discover I-cs f -networks.
The following main results are obtained: (1) A space X has an I-cs f
-network if and only if X is a continuous and I-covering image of a metric
space. (2) A space X is an I-cs f -countable space if and only if X is a
continuous I-covering and boundary s-image of a metric space. (3) A space X
has a point-countable I-cs-network if and only if X is a continuous
I-covering and s-image of a metric space.
Publisher
National Library of Serbia
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