Topological spaces induced by homotopic distance
محورهای موضوعی : Algebraic topology
T. Vergili
1
(
Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon, Turkey
)
A. Borat
2
(
Department of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University, Bursa, Turkey
)
کلید واژه: Metric spaces, Topological complexity, Homotopic distance, Lusternik Schnirelmann category,
چکیده مقاله :
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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