Shape dimension of maps
Pavel S. Gevorgyan, I. Pop
TL;DR
This paper introduces the shape dimension of maps, a new invariant generalizing topological shape dimension, explores its properties, and provides examples including a surjective map between shape infinite-dimensional spaces.
Contribution
It defines the shape dimension of maps, investigates its properties, and solves the problem of increasing shape dimension via shape finite-dimensional maps.
Findings
Shape dimension generalizes topological shape dimension.
The paper proves properties of shape dimension.
An example of a surjective map between shape infinite-dimensional spaces is provided.
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.
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Taxonomy
TopicsImage Retrieval and Classification Techniques · Digital Image Processing Techniques · Advanced Numerical Analysis Techniques