Topological spaces induced by homotopic distance

Journal of Linear and Topological Algebra

دوره 11، شماره 02، شهریور 2022، صفحه 85-91   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2022.1955292.1482

نویسندگان

T. Vergili^{* 1}؛ A. Borat²

¹Department of Mathematics‎, ‎Faculty of Science‎, ‎Karadeniz Technical University‎, ‎Trabzon‎, ‎Turkey

²Department of Mathematics‎, ‎Faculty of Engineering and Natural Sciences‎, ‎Bursa Technical University‎, ‎Bursa‎, ‎Turkey

چکیده

‎Topological complexity which plays an important role in motion planning problem can be generalized to homotopic distance $\mathrm{D}$ as introduced in \cite{MVML}‎. ‎In this paper‎, ‎we study the homotopic distance and mention that it can be realized as a pseudometric on $\mathrm{Map}(X,Y)$‎. ‎Moreover we study the topology induced by the pseudometric $\mathrm{D}$‎. ‎In particular‎, ‎we consider the space $\mathrm{Map}(S^1,S^1)$ and use the non-compactness of it to talk about the non-compactness of $\mathrm{Map}(X,Y)$‎.
 

کلیدواژه‌ها

Homotopic distance؛ metric spaces؛ topological complexity؛ Lusternik Schnirelmann category

مراجع

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