Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 21-28
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A. V. Arkhangel'skii; D. V. Ranchin. Everywhere dense subspaces of topological products and properties associated with final compactness. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 21-28. http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a4/
@article{VMUMM_1982_6_a4,
author = {A. V. Arkhangel'skii and D. V. Ranchin},
title = {Everywhere dense subspaces of topological products and properties associated with final compactness},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {21--28},
year = {1982},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a4/}
}
TY - JOUR
AU - A. V. Arkhangel'skii
AU - D. V. Ranchin
TI - Everywhere dense subspaces of topological products and properties associated with final compactness
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1982
SP - 21
EP - 28
IS - 6
UR - http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a4/
LA - ru
ID - VMUMM_1982_6_a4
ER -
%0 Journal Article
%A A. V. Arkhangel'skii
%A D. V. Ranchin
%T Everywhere dense subspaces of topological products and properties associated with final compactness
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1982
%P 21-28
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a4/
%G ru
%F VMUMM_1982_6_a4
We prove the following. The $\sigma$–product of a family $\mathfrak{U}$ of topological spaces with countable base is a Lindelöf $\Sigma$-space if and only if $\mathfrak{U}$ has at most $2^{\aleph_0}$ non-homeomorphic elements. The $\sigma$-product of $\mathscr{K}$-analytical spaces is itself $\mathscr{K}$-analytical. Let $X$ be a $\sigma$-product of Lindelöf $\Sigma$-spaces and $C_p(X)$ the space of all continuous real-valued functions on $X$ in the topology of pointwise convergence. Then every bicompact $f\subset C_p(X)$ is a Frechet–Uryson space.
