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On Blumberg’s theorem

Ofelia Teresa Alas — 1976

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

Si stabilisce un'estensione di un teorema di Blumberg includente altre più o meno recenti estensioni [4, 5, 2].

Properties of two cardinal topological invariants

Ofelia Teresa Alas — 1971

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

Si stabiliscono proprietà di due invarianti topologici riferiti, rispettivamente, alla intersezione di una collezione d'insiemi aperti ed ai ricoprimenti aperti localmente finiti di uno spazio.

Density and continuous functions. Nota II

Ofelia Teresa Alas — 1970

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

Relazione tra un tipo particolare di prodotto di spazi topologici e le funzioni θ -continue. Dimostrazione di un risultato generalizzante un teorema di A.M. Gleason.

On compact metrisable spaces

Ofelia Teresa Alas — 1971

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

Si assegnano condizioni atte ad assicurare la metrizzabilità di uno spazio di Hausdorff.

Addition theorems, D -spaces and dually discrete spaces

Ofelia Teresa AlasVladimir Vladimirovich TkachukRichard Gordon Wilson — 2009

Commentationes Mathematicae Universitatis Carolinae

A in a space X is a family 𝒪 = { O x : x X } of open subsets of X such that x O x for any x X . A set Y X is if 𝒪 ( Y ) = { O x : x Y } = X . If every neighbourhood assignment in X has a closed and discrete (respectively, discrete) kernel, then X is said to be a D -space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf P -space is a D -space and we prove an addition theorem for metalindelöf spaces which...

Extraresolvability and cardinal arithmetic

Ofelia Teresa AlasSalvador García-FerreiraArtur Hideyuki Tomita — 1999

Commentationes Mathematicae Universitatis Carolinae

Following Malykhin, we say that a space X is if X contains a family 𝒟 of dense subsets such that | 𝒟 | > Δ ( X ) and the intersection of every two elements of 𝒟 is nowhere dense, where Δ ( X ) = min { | U | : U is a nonempty open subset of X } is the of X . We show that, for every cardinal κ , there is a compact extraresolvable space of size and dispersion character 2 κ . In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) 2 κ < 2 κ + , 2) ( κ + ) κ is extraresolvable and 3) A ( κ + ) κ is extraresolvable, where A ( κ + ) ...

Connectedness and local connectedness of topological groups and extensions

Ofelia Teresa AlasMihail G. TkachenkoVladimir Vladimirovich TkachukRichard Gordon Wilson — 1999

Commentationes Mathematicae Universitatis Carolinae

It is shown that both the free topological group F ( X ) and the free Abelian topological group A ( X ) on a connected locally connected space X are locally connected. For the Graev’s modification of the groups F ( X ) and A ( X ) , the corresponding result is more symmetric: the groups F Γ ( X ) and A Γ ( X ) are connected and locally connected if X is. However, the free (Abelian) totally bounded group F T B ( X ) (resp., A T B ( X ) ) is not locally connected no matter how “good” a space X is. The above results imply that every non-trivial continuous homomorphism...

On dense subspaces satisfying stronger separation axioms

We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than c has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight c which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of π -weight less than 𝔭 has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...

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