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Diagonal conditions in ordered spaces

Harold Bennett, David Lutzer (1997)

Fundamenta Mathematicae

For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each T ⊂ X 2 - Δ ( X ) with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If ω 1 ∈ D ( X ) then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems...

Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras

Michael M. Zarichnyi (1991)

Commentationes Mathematicae Universitatis Carolinae

We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.

Eberlein spaces of finite metrizability number

István Juhász, Zoltán Szentmiklóssy, Andrzej Szymański (2007)

Commentationes Mathematicae Universitatis Carolinae

Yakovlev [On bicompacta in Σ -products and related spaces, Comment. Math. Univ. Carolin. 21.2 (1980), 263–283] showed that any Eberlein compactum is hereditarily σ -metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.

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

Ondřej F. K. Kalenda (1999)

Commentationes Mathematicae Universitatis Carolinae

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.

Equilateral sets in Banach spaces of the form C(K)

Sophocles K. Mercourakis, Georgios Vassiliadis (2015)

Studia Mathematica

We show that for "most" compact nonmetrizable spaces, the unit ball of the Banach space C(K) contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces K such that the minimum cardinality of a maximal equilateral set in C(K) is countable.

Fiber orders and compact spaces of uncountable weight

Antonio Avilés, Ondřej F. K. Kalenda (2009)

Fundamenta Mathematicae

We study an order relation on the fibers of a continuous map and its application to the study of the structure of compact spaces of uncountable weight.

Function spaces and local properties

Ziqin Feng, Paul Gartside (2013)

Fundamenta Mathematicae

Necessary conditions and sufficient conditions are given for C p ( X ) to be a (σ-) m₁- or m₃-space. (A space is an m₁-space if each of its points has a closure-preserving local base.) A compact uncountable space K is given with C p ( K ) an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).

Function spaces on τ -Corson compacta and tightness of polyadic spaces

Murray G. Bell, W. Marciszewski (2004)

Czechoslovak Mathematical Journal

We apply the general theory of τ -Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness τ . In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.

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