Geodesic
On function spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 999-1008

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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. 
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     author = {Yu. L. Ershov and M. V. Schwidefsky},
     title = {On function spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {999--1008},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a21/}
}
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Yu. L. Ershov; M. V. Schwidefsky. On function spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 999-1008. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a21/