Abstract: Consider the following properties of topological T0-spaces: (1) to be a d-space; (2) to be a topological join-semilattice; (3) to be a sober space; (4) to be an essentially complete space; (5) to be a [restricted] injective space; (6) to be a [sober] ∆-space. Let P denote one of the properties (1)–(4). Then a T0-space Y has P if and only if C(X, Y) has P for some (and therefore for each) T0-space X. Let Q denote one of the properties (5)–(6). Then a T0-space Y has Q if and only if C(X, Y) has Q for some (and therefore for each) α ∗ -space X. A T0-space Y is a [sober] ∆-space if and only if C(X, Y) is a [sober] ∆-space for some (and therefore for each) ∆-space X. Both authors were supported by the fundamental research program of the Siberian Branch of the Russian Academy of Sciences I.1.1, project 0314-2019-0003, and by RFBF, project 18-01-00624a. References [1] Ershov Yu. L. Topology for Discrete Mathematics. SB RAS Publishing House, Novosibirsk, 2020. [2] Ershov Yu. L., Schwidefsky M. V. On function spaces // Siberian Electronic Mathematical Reports. 2020. Vol. 17. P. 999–1008. Available at http://semr.math.nsc.ru/v17/p999-1008.pdf

Cite: Ershov Y.L. , Schwidefsky M.V.
On function spaces
In compilation Международная конференция МАЛЬЦЕВСКИЕ ЧТЕНИЯ 16–20 ноября 2020 г. Тезисы докладов. 2020. – C.244.

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