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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 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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