Shape dimension of maps
Algebraic Topology
2023-08-29 v1
Abstract
In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The question of raising the shape dimension by shape finite-dimensional maps is solved. An example of a shape finite-dimensional surjective map between shape infinite-dimensional spaces is given.
Cite
@article{arxiv.2308.13843,
title = {Shape dimension of maps},
author = {Pavel S. Gevorgyan and I. Pop},
journal= {arXiv preprint arXiv:2308.13843},
year = {2023}
}
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8 pages