On structural numbers of topological spaces
Vitalij Chatyrko, Alexandre Karassev

TL;DR
This paper introduces and analyzes structural numbers related to topological spaces, extending previous concepts to subclasses of hereditarily normal spaces, and provides bounds for these numbers in metrizable and countable-dimensional spaces.
Contribution
It defines new structural numbers for subclasses of hereditarily normal spaces and establishes bounds for these numbers in specific classes of metrizable and countable-dimensional spaces.
Findings
For any metrizable space with dimension n, the structural number is between 1 and n+1.
For countable-dimensional metrizable spaces, the structural number is between 1 and aleph_0.
The paper extends the concept of structural numbers to subclasses of hereditarily normal T_1-spaces.
Abstract
Zero-dimensional structural numbers and w.r.t. dimensions and were introduced by Georgiou, Hattori, Megaritis, and Sereti. Somewhat similarly, we define structural numbers for different subclasses of the class of hereditarily normal -spaces. In particular, we show that: (a) for any metrizable space with we have ; (b) for any countable-dimensional metrizable space we have , where is the class of metrizable spaces with
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Taxonomy
TopicsFuzzy and Soft Set Theory
