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


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


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


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


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


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


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...