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Proper actions of locally compact groups on equivariant absolute extensors

Sergey Antonyan (2009)

Fundamenta Mathematicae

Let G be a locally compact Hausdorff group. We study equivariant absolute (neighborhood) extensors (G-AE's and G-ANE's) in the category G-ℳ of all proper G-spaces that are metrizable by a G-invariant metric. We first solve the linearization problem for proper group actions by proving that each X ∈ G-ℳ admits an equivariant embedding in a Banach G-space L such that L∖{0} is a proper G-space and L∖{0} ∈ G-AE. This implies that in G-ℳ the notions of G-A(N)E and G-A(N)R coincide. Our embedding result...

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 Q.

Bandy, C. (1991)

International Journal of Mathematics and Mathematical Sciences

Proximal set-open topologies

Anna Di Concilio, Som Naimpally (2000)

Bollettino dell'Unione Matematica Italiana

Introduciamo una nuova classe di topologie in spazi di funzioni derivanti da prossimità sul rango, che denotiamo sinteticamente PSOTs, acronimo di proximal set-open topologies. Le PSOTs sono una naturale generalizzazione delle classiche topologie di tipo set-open quando l'ordinaria inclusione viene sostituita con l'inclusione stretta associata ad una prossimità. Molte e note topologie di tipo set-open connesse a speciali networks sono esempi di PSOTs. Ogni PSOT è contraibile ad un sottospazio chiuso...

Pseudocompactness and the cozero part of a frame

Bernhard Banaschewski, Christopher Gilmour (1996)

Commentationes Mathematicae Universitatis Carolinae

A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a σ -frame and to Alexandroff spaces.

Pseudo-homotopies of the pseudo-arc

Alejandro Illanes (2012)

Commentationes Mathematicae Universitatis Carolinae

Let X be a continuum. Two maps g , h : X → X are said to be pseudo-homotopic provided that there exist a continuum C , points s , t ∈ C and a continuous function H : X × C → X such that for each x ∈ X , H ( x , s ) = g ( x ) and H ( x , t ) = h ( x ) . In this paper we prove that if P is the pseudo-arc, g is one-to-one and h is pseudo-homotopic to g , then g = h . This theorem generalizes previous results by W. Lewis and M. Sobolewski.

Pseudouniform topologies on C ( X ) given by ideals

Roberto Pichardo-Mendoza, Angel Tamariz-Mascarúa, Humberto Villegas-Rodríguez (2013)

Commentationes Mathematicae Universitatis Carolinae

Given a Tychonoff space X , a base α for an ideal on X is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on α converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

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