Linear subspace of Rl without dense totally disconnected subsets

K. Ciesielski

Displaying similar documents to “Linear subspace of Rl without dense totally disconnected subsets”

Forcing countable networks for spaces satisfying $R (X^{ω}) = ω$

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (1996)

Commentationes Mathematicae Universitatis Carolinae

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We show that all finite powers of a Hausdorff space $X$ do not contain uncountable weakly separated subspaces iff there is a c.c.c poset $P$ such that in $V^{P}$ $X$ is a countable union of $0$ -dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of $X$ .

A generalization of a generic theorem in the theory of cardinal invariants of topological spaces

Alejandro Ramírez-Páramo, Noé Trinidad Tapia-Bonilla (2007)

Commentationes Mathematicae Universitatis Carolinae

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The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If $X$ is a $T_{2}$ -space, then $| X | \leq 2^{L (X) χ (X)}$ . Moreover, we will show relative versions of three well-known cardinal inequalities.

Embedding of the ordinal segment $[0, ω_{1}]$ into continuous images of Valdivia compacta

Ondřej F. K. Kalenda (1999)

Commentationes Mathematicae Universitatis Carolinae

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We prove in particular that a continuous image of a Valdivia compact space is Corson provided it contains no homeomorphic copy of the ordinal segment $[0, ω_{1}]$ . This generalizes a result of R. Deville and G. Godefroy who proved it for Valdivia compact spaces. We give also a refinement of their result which yields a pointwise version of retractions on a Valdivia compact space.

Displaying similar documents to “Linear subspace of Rl without dense totally disconnected subsets”

Forcing countable networks for spaces satisfying R ( X ω ) = ω

A generalization of a generic theorem in the theory of cardinal invariants of topological spaces

Embedding of the ordinal segment [ 0 , ω 1 ] into continuous images of Valdivia compacta

Forcing countable networks for spaces satisfying $R (X^{ω}) = ω$

Embedding of the ordinal segment $[0, ω_{1}]$ into continuous images of Valdivia compacta