Generalization of Kuratowski problem in linear spaces
Allahkaram Shafie
TL;DR
This paper investigates the Kuratowski problem within vector spaces, establishing that the maximum number of distinct sets generated from a convex set through algebraic closure and complement operations is eight.
Contribution
It extends the Kuratowski problem to linear spaces and determines the maximum number of distinct sets obtainable through algebraic operations.
Findings
Maximum of 8 distinct sets generated from one convex set
Application of algebraic closure and complement in linear spaces
Extension of Kuratowski problem to vector spaces
Abstract
In this short paper, Kuratowski problem will be investigated in vector space. The highest number of distinct sets that can be generated from one convex set in linear space by repeatedly applying algebraic closure and complement in any order is 8. Keywords: Kuratowski problem, algebraic interior, algebraic closure
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Taxonomy
TopicsGeotechnical and Mining Engineering · Industrial and Mining Safety · Mathematical functions and polynomials