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 | ≤ 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.

More topological cardinal inequalities

O. Alas (1993)

Colloquium Mathematicae

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A new topological cardinal invariant is defined; it may be considered as a weaker form of the Lindelöf degree.

On D-dimension of metrizable spaces

Wojciech Olszewski (1991)

Fundamenta Mathematicae

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For every cardinal τ and every ordinal α, we construct a metrizable space M α ( τ ) and a strongly countable-dimensional compact space Z α ( τ ) of weight τ such that D ( M α ( τ ) ) ≤ α , D ( Z α ( τ ) ) ≤ α and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of M α ( τ ) and to a subspace of Z α + 1 ( τ ) .