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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 ) τ and nw ( K ) τ , then there exists a Tychonoff (regular) topology 𝒯 * 𝒯 such that w ( L , 𝒯 * ) τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

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...

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