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Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

Let $(L, 𝒯)$ be a Tychonoff (regular) paratopological group or algebra over a field or ring $K$ or a topological semigroup. If $nw (L, 𝒯) \leq τ$ and $nw (K) \leq τ$ , then there exists a Tychonoff (regular) topology $𝒯^{*} \subseteq 𝒯$ such that $w (L, 𝒯^{*}) \leq τ$ and $(L, 𝒯^{*})$ is a paratopological group, algebra over $K$ or a topological semigroup respectively.

Configurations of points in sets of positive measure and in Baire sets of second category

François Destrempes, Ambar Sengupta (1989)

Fundamenta Mathematicae

Connected groups with polynomially induced dual.

J. Boidol (1982)

Journal für die reine und angewandte Mathematik

Continuity of semigroup actions.

D. Helmer (1981)

Semigroup forum

Contractive Automorphisms on Locally Compact Groups.

Eberhard Siebert (1986)

Mathematische Zeitschrift

Covering locally compact groups by less than $2^{ω}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if $C_{E K}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of $C_{E K}$ . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...