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This article is cited in 3 scientific papers (total in 3 papers)
Mathematical logic, algebra and number theory
On function spaces
Yu. L. Ershova, M. V. Schwidefskyab a Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
b Novosibirsk State Technical University, 20, K. Marx ave., Novosibirsk, 630073, Russia
Abstract:
For certain properties $\mathfrak{P}$ of topological $T_0$-spaces, we prove that an arbitrary $T_0$-space $\mathbb{Y}$ has property $\mathfrak{P}$ if and only if the function space $\mathbb{C}(\mathbb{X},\mathbb{Y})$ endowed with the pointwise convergence topology possesses $\mathfrak{P}$ for some (and therefore, for each) $[\alpha^\ast-]$space $\mathbb{X}$.
Keywords:
$d$-space, essentially complete space, function space, injective space, sober space, $T_0$-space.
Received March 5, 2020, published July 21, 2020
Citation:
Yu. L. Ershov, M. V. Schwidefsky, “On function spaces”, Sib. Èlektron. Mat. Izv., 17 (2020), 999–1008
Linking options:
https://www.mathnet.ru/eng/semr1268 https://www.mathnet.ru/eng/semr/v17/p999
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Abstract page: | 324 | Full-text PDF : | 89 | References: | 19 |
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