Displaying similar documents to “Condensations of Tychonoff universal topological algebras”

Cellularity and the index of narrowness in topological groups

Mihail G. Tkachenko (2011)

Commentationes Mathematicae Universitatis Carolinae

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We study relations between the cellularity and index of narrowness in topological groups and their G δ -modifications. We show, in particular, that the inequalities in ( ( H ) τ ) ≤ 2 τ · in ( H ) and c ( ( H ) τ ) ≤ 2 2 τ · in ( H ) hold for every topological group H and every cardinal τ ≥ ω , where ( H ) τ denotes the underlying group H endowed with the G τ -modification of the original topology of H and in ( H ) is the index of narrowness of the group H . Also, we find some bounds for the complexity of continuous real-valued functions f on an arbitrary ω -narrow group...

Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

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We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property α 1 . 5 is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C p ( X ) of continuous real-valued functions on X with the...

On the cardinality of functionally Hausdorff spaces

Alessandro Fedeli (1996)

Commentationes Mathematicae Universitatis Carolinae

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In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If X is a functionally Hausdorff space then | X | ≤ 2 f s ( X ) ψ τ ( X ) ; (ii) Let X be a functionally Hausdorff space with f s ( X ) ≤ κ . Then there is a subset S of X such that | S | ≤ 2 κ and X = ⋃ { c l τ θ ( A ) : A ∈ [ S ] ≤ κ } .

Generalization of the topological algebra ( C b ( X ) , β )

Jorma Arhippainen, Jukka Kauppi (2009)

Studia Mathematica

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We study subalgebras of C b ( X ) equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies ξ on a fixed infinite dimensional vector space E such that ( E , ξ ) has not the Hahn-Banach extension property but the topological dual ( E , ξ ) ' separates points of E from zero is given.

Extremal phenomena in certain classes of totally bounded groups

W. W. Comfort, Lewis C. Robertson

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For various pairs of topological properties such that P ⇒ Q, we consider two questions: (A) Does every topological group topology with P extend properly to a topological group topology with Q, and (B) must a topological group with P have a proper dense subgroup with Q? We obtain negative results and positive results. Principal among the latter is the statement that any pseudocompact group G of uncountable weight which satisfies any of the following three conditions has both a strictly...