Properties of some generalizations of the notion of continuity of a function
In questo articolo vengono presentate e studiate le nozioni di insieme e di insieme -chiuso. Inoltre, vengono introdotte le nozioni di -continuità, -compatezza e -connessione e vengono fornite alcune caratterizzazioni degli spazi e . Infine, viene mostrato che gli spazi -connessi e -compatti vengono preservati mediante suriezioni -continue.
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...
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 -frame and to Alexandroff spaces.
Let be a continuum. Two maps are said to be pseudo-homotopic provided that there exist a continuum , points and a continuous function such that for each , and . In this paper we prove that if is the pseudo-arc, is one-to-one and is pseudo-homotopic to , then . This theorem generalizes previous results by W. Lewis and M. Sobolewski.
Given a Tychonoff space , a base for an ideal on is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on 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.
The main results presented in this paper concern multivalued maps. We consider the cliquishness, quasicontinuity, almost continuity and almost quasicontinuity; these properties of multivalued maps are characterized by the analogous properties of some real functions. The connections obtained are used to prove decomposition theorems for upper and lower quasicontinuity.