Year: 2025
Type: article
Abstract: In this paper, we transfer the problem of measuring navigational complexity in topological spaces to the nearness theory. We investigate the most important component of this problem, the topological complexity number (denoted by TC), with its different versions including relative and higher TC, on the proximal Schwarz genus as well as the proximal (higher) homotopic distance. We outline the fundamental properties of some concepts related to the proximal (or descriptive proximal) TC numbers. In addition, we provide some instances of (descriptive) proximity spaces, specifically on basic robot vacuum cleaners, to illustrate the results given on proximal and descriptive proximal TC.
Source: Applied General Topology
Authors: Melih İs, İsmet Karaca
Institution: Ege University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G7238306563
OpenAlex ID: W4409058786