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On families of Lindelöf and related subspaces of 2 ω ₁

Lúcia Junqueira, Piotr Koszmider (2001)

Fundamenta Mathematicae

We consider the families of all subspaces of size ω₁ of 2 ω ₁ (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in [ X ] ω ₁ are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used...

On finite powers of countably compact groups

Artur Hideyuki Tomita (1996)

Commentationes Mathematicae Universitatis Carolinae

We will show that under M A c o u n t a b l e for each k ∈ ℕ there exists a group whose k -th power is countably compact but whose 2 k -th power is not countably compact. In particular, for each k ∈ ℕ there exists l ∈ [ k , 2 k ) and a group whose l -th power is countably compact but the l + 1 -st power is not countably compact.

On locales whose countably compact sublocales have compact closure

Themba Dube (2023)

Mathematica Bohemica

Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called cl -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.

On locally S -closed spaces

Takashi Noiri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente S -chiuso sia localmente S -chiuso.

On monotone Lindelöfness of countable spaces

Ronnie Levy, Mikhail Matveev (2008)

Commentationes Mathematicae Universitatis Carolinae

A space is monotonically Lindelöf (mL) if one can assign to every open cover 𝒰 a countable open refinement r ( 𝒰 ) so that r ( 𝒰 ) refines r ( 𝒱 ) whenever 𝒰 refines 𝒱 . We show that some countable spaces are not mL, and that, assuming CH, there are countable mL spaces that are not second countable.

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