Document Type : Research Paper

Authors

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

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

Abstract

‎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 $\mathrm{Map}(X,Y)$‎.

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