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Products of Lindelöf T 2 -spaces are Lindelöf – in some models of ZF

Horst Herrlich (2002)

Commentationes Mathematicae Universitatis Carolinae

The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, • amusing that finite summability of the Lindelöf property takes place if either some weak choice principle...

Products of topological spaces and families of filters

Paolo Lipparini (2023)

Commentationes Mathematicae Universitatis Carolinae

We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by ≤ ω 1 factors are Lindelöf. Parallel results are obtained for final ω n -compactness, [ λ , μ ] -compactness, the Menger and the Rothberger properties.

Properties of Λ , δ -closed sets in topological spaces

D. N. Georgiou, S. Jafari, T. Noiri (2004)

Bollettino dell'Unione Matematica Italiana

In questo articolo vengono presentate e studiate le nozioni di insieme Λ δ e di insieme Λ , δ -chiuso. Inoltre, vengono introdotte le nozioni di Λ , δ -continuità, Λ , δ -compatezza e Λ , δ -connessione e vengono fornite alcune caratterizzazioni degli spazi δ - T 0 e δ - T 1 . Infine, viene mostrato che gli spazi Λ , δ -connessi e Λ , δ -compatti vengono preservati mediante suriezioni δ -continue.

Property ( a ) and dominating families

Samuel Gomes da Silva (2005)

Commentationes Mathematicae Universitatis Carolinae

Generalizations of earlier negative results on Property ( a ) are proved and two questions on an ( a ) -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ 2 ω is regular” and “ 2 ω < 2 ω 1 ” the existence of a T 1 separable locally compact ( a ) -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants...

Property D and pseudonormality in first countable spaces

Alan S. Dow (2005)

Commentationes Mathematicae Universitatis Carolinae

In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin’s Axiom type principle P ( c ) . We show that there is no such space in the usual Cohen model of the failure of CH.

Proto-metrizable fuzzy topological spaces

Francisco Gallego Lupiañez (1999)

Kybernetika

In this paper we define for fuzzy topological spaces a notion corresponding to proto-metrizable topological spaces. We obtain some properties of these fuzzy topological spaces, particularly we give relations with non-archimedean, and metrizable fuzzy topological spaces.

Currently displaying 41 – 60 of 64