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The famous Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space, has remained unsolved for 85 years, though it has been answered in the affirmative for reflexive Banac
Externí odkaz:
http://arxiv.org/abs/1707.09546
We prove that if $H$ is a topological group such that all closed subgroups of $H$ are separable, then the product $G\times H$ has the same property for every separable compact group $G$. Let $c$ be the cardinality of the continuum. Assuming $2^{\omeg
Externí odkaz:
http://arxiv.org/abs/1701.00084
Early this century K. H. Hofmann and S. A. Morris introduced the class of pro-Lie groups which consists of projective limits of finite-dimensional Lie groups and proved that it contains all compact groups, all locally compact abelian groups, and all
Externí odkaz:
http://arxiv.org/abs/1605.05279
Autor:
Tkachenko, Mikhail G., Xie, Li-Hong
Publikováno v:
In Topology and its Applications 1 September 2021 301
Autor:
Tkachenko, Mikhail G.
We show that if $Y$ is a dense subspace of a Tychonoff space $X$, then $w(X)\leq nw(Y)^{Nag(Y)}$, where $Nag(Y)$ is the Nagami number of $Y$. In particular, if $Y$ is a Lindel\"of $\Sigma$-space, then $w(X)\leq nw(Y)^\omega\leq nw(X)^\omega$. Better
Externí odkaz:
http://arxiv.org/abs/1509.02874
We prove that, under CH, any space with a regular $G_\delta$-diagonal and caliber $\omega_1$ is separable; a corollary of this result answers, under CH, a question of Buzyakova. For any Urysohn space $X$, we establish the inequality $|X|\le wL(X)^{s\
Externí odkaz:
http://arxiv.org/abs/1506.04665
A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie groups which co
Externí odkaz:
http://arxiv.org/abs/1501.02877
Publikováno v:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM; Jul2024, Vol. 118 Issue 3, p1-16, 16p
Publikováno v:
In Topology and its Applications 1 June 2018 241:89-101