Displaying similar documents to “On locally r -incomparable families of infinite-dimensional Cantor manifolds”

Generalized linearly ordered spaces and weak pseudocompactness

Oleg Okunev, Angel Tamariz-Mascarúa (1997)

Commentationes Mathematicae Universitatis Carolinae

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A space X is if X is either weakly pseudocompact or Lindelöf locally compact. We prove that if X is a generalized linearly ordered space, and either (i) each proper open interval in X is truly weakly pseudocompact, or (ii) X is paracompact and each point of X has a truly weakly pseudocompact neighborhood, then X is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].

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.

Intersection topologies with respect to separable GO-spaces and the countable ordinals

M. Jones (1995)

Fundamenta Mathematicae

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Given two topologies, T 1 and T 2 , on the same set X, the intersection topologywith respect to T 1 and T 2 is the topology with basis U 1 ∩ U 2 : U 1 ∈ T 1 , U 2 ∈ T 2 . Equivalently, T is the join of T 1 and T 2 in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and ω 1 -compactness in this class of topologies. We demonstrate that the majority of his results...

On the cardinality and weight spectra of compact spaces, II

Istvan Juhász, Saharon Shelah (1998)

Fundamenta Mathematicae

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Let B(κ,λ) be the subalgebra of P(κ) generated by [ κ ] ≤ λ . It is shown that if B is any homomorphic image of B(κ,λ) then either | B | < 2 λ or | B | = | B | λ ; moreover, if X is the Stone space of B then either | X | ≤ 2 2 λ or | X | = | B | = | B | λ . This implies the existence of 0-dimensional compact T 2 spaces whose cardinality and weight spectra omit lots of singular cardinals of “small” cofinality.

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 .

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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 Let F i = 1 , . . . , N be affine mappings of ℝ n . It is well known that if there exists j ≤ 1 such that for every σ 1 , . . . , σ j ∈ 1 , . . . , N the composition (1) F σ 1 ∘ . . . ∘ F σ j is a contraction, then for any infinite sequence σ 1 , σ 2 , . . . ∈ 1 , . . . , N and any z ∈ ℝ n , the sequence (2) F σ 1 ∘ . . . ∘ F σ n ( z ) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any z ∈ ℝ n and any σ = σ 1 , σ 2 , . . . belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every σ = σ 1 , σ 2 , . . . ∈ Σ the composition (1) is a contraction....