Geodesic
The limitation topology and the functor $C(X,Y)$
Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 57-62.

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We consider the category $\mathbf{\Pi}$ where the objects are pairs of topological spaces $(X,Y)$ and the morphisms of a pair $(X,Y)$ to a pair $(E,Z)$ are pairs of continuous maps $(\varphi,\psi)$ where $\varphi :E\mapsto X$, $\psi:Y\mapsto Z$. The space of continuous maps $C_{Lim} (X,Y)$ with the limitation topology defined by H. Torunczyk is assigned to each pair $(X,Y)$. It is proved that this correspondence determines a covariant functor $C_{Lim}$ from the category $\mathbf{\Pi}$ to the category $Top$ of topological spaces with continuous maps. Necessary and sufficient conditions are found to distinguish the subcategory $\mathcal{K}\subset\mathbf{\Pi}$ on which the functor $C_{Lim}$ is continuous. 
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H. O. Kukrak; V. L. Timokhovich. The limitation topology and the functor $C(X,Y)$. Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 57-62. http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a5/

[1] Timokhovich V. L., Frolova D. S., “Topologii ravnomernoi skhodimosti. Sobstvennost (v smysle Arensa-Dugundzhi) i sekventsialnaya sobstvennost”, Izv. vuzov. Matem., 2013, no. 9, 45–57 | MR | Zbl

[2] Timokhovich V. L., Frolova D. S., “O svoistvakh infimalnoi topologii prostranstva otobrazhenii”, Izv. vuzov. Matem., 2016, no. 4, 87–99 | MR | Zbl

[3] Kukrak G. O., Timokhovich V. L., Frolova D. S., “Nekotorye topologicheskie svoistva funktora $C(X,Y)$”, Trudy inst. matem. NAN Belarusi, 26:1 (2018), 71–78 | MR

[4] Kukrak G. O., Timokhovich V. L., “O nepreryvnosti funktorov vida $C(X,Y)$”, Zhurnal Bel.gos.universiteta. Matematika, informatika, 2020, no. 1, 22–29 | MR

[5] Torunczyk H., “Characterizing Hilbert space topology”, Fundam. math., 111:3 (1981), 247–262 | DOI | MR | Zbl

[6] Fedorchuk V. V., Chigogidze A. Ch., Absolyutnye retrakty i beskonechnomernye mnogoobraziya, Nauka, M., 1992

[7] Bowers P., “Limitation topologies on function spaces”, Trans. Amer. Math. Soc., 314:1 (1989), 421–431 | DOI | MR | Zbl

[8] Sakai K., Geometric Aspects of General Topology, Springer, Japan, 2013 | MR | Zbl

[9] Bacon P., “The compactness of countably compact spaces”, Pacific J. Math., 32:3 (1970), 587–592 | DOI | MR | Zbl

[10] Kukrak G. O., Timokhovich V. L., “O predele obratnogo spektra eksponentsialnykh prostranstv”, Vestn. BGU. Ser. 1, 2001, no. 1, 51–55 | MR | Zbl

[11] Frolova D. S., “O sekventsialno sobstvennykh topologiyakh prostranstva otobrazhenii”, Trudy inst.matem. NAN Belarusi, 21:1 (2013), 102–108 | Zbl

[12] Engelking R., Obschaya topologiya, Mir, M., 1986