Si provano nuovi risultati riguardanti gli «-sets» e gli spazi «Near-compact». Si completano alcune ricerche pubblicate dai primi due autori nel 1978 e si risolvono due problemi recentemente posti da Cammaroto, Gutierrez, Nordo e Prada.
Let be the large source of epimorphisms in the category of Urysohn spaces constructed in [2]. A sink is called natural, if for all . In this paper natural sinks are characterized. As a result it is shown that permits no -factorization structure for arbitrary (large) sources.
Assuming OCA, we shall prove that for some pairs of Fréchet -spaces , the Fréchetness of the product implies that is . Assuming MA, we shall construct a pair of spaces satisfying the assumptions of the theorem.
We prove that if ℱ is a non-meager P-filter, then both ℱ and are countable dense homogeneous spaces.
We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.
Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of .
One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.