Set-valued maps and some generalized metric spaces
Er-Guang Yang

TL;DR
This paper characterizes various generalized metric spaces, including stratifiable and semi-metrizable spaces, using set-valued maps with strictly increasing closed covers, extending the understanding of their structure and related real-valued functions.
Contribution
It introduces new characterizations of generalized metric spaces via set-valued maps with strictly increasing closed covers, broadening the theoretical framework.
Findings
Characterization of stratifiable and semi-metrizable spaces using set-valued maps.
Extension of characterizations to spaces with generalized real-valued functions.
Application of these characterizations to understand boundedness and structure of such spaces.
Abstract
To give characterizations of monotonically countably paracompact spaces with set-valued maps, Yamazaki [22] introduced the notion of strictly increasing closed cover of a topological space with which the boundedness of a set-valued map was defined. In this paper, we show that most of generalized metric spaces such as stratifiable spaces, semi-metrizable spaces can be characterized with set-valued maps with values into the family of all closed nonempty subsets of a space which has a strictly increasing closed cover. Moreover, as an application, we use the results obtained to give characterizations of the corresponding spaces with generalized real-valued functions.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fixed Point Theorems Analysis
