Geodesic
Some topological properties of the functor $C(X,Y)$
Trudy Instituta matematiki, Tome 26 (2018) no. 1, pp. 71-78 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mathcal{K}$ is a category which objects are some pairs of topological spaces $(X,Y).$ To every pair $(X,Y)$ we associate a space $C_\tau(X,Y)$ of continuous maps endowed with some topology $\tau,$ and to every morphism $\mathcal{K}$ corresponding connecting maps between $C\tau(X,Y)$ spaces. In this paper we study the possibility of the defined map from $\mathcal{K}$ to category $Top$ of topological spaces and continuous maps to be a functor and its continuity. 
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H. O. Kukrak; V. L. Timokhovich; D. S. Frolova. Some topological properties of the functor $C(X,Y)$. Trudy Instituta matematiki, Tome 26 (2018) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/TIMB_2018_26_1_a9/

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