Non-constant continuous maps of modifications of topological spaces
Non-meager P-filters are countable dense homogeneous
We prove that if ℱ is a non-meager P-filter, then both ℱ and are countable dense homogeneous spaces.
Non-normality and relative normality of Niemytzki plane
Non-separating subcontinua of planar continua
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.
Non-Unique Fixed Points In L-Spaces
Non-unique fixed points in L-spaces.
Normal P-spaces and the -topology
Normal subspaces in products of two ordinals
Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of .
Normal Vietoris implies compactness: a short proof
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.
Normality and hereditary countable paracompactness of Pixley-Roy hyperspaces
Normality and Martin's axiom
Normality and paracompactness in finite and countable Cartesian products
Normality and paracompactness in subsets of product spaces
Normality and paracompactness of Pixley-Roy hyperspaces
Normality of product spaces
Not all dyadic spaces are supercompact
Note about atom-categories of topological spaces
Note on category in Cartesian products of metrizable spaces
Note on decompositions of metrizable spaces I
Note on the Wijsman hyperspaces of completely metrizable spaces
We consider the hyperspace of nonempty closed subsets of completely metrizable space endowed with the Wijsman topologies . If is separable and , are two metrics generating the topology of , every countable set closed in has isolated points in . For , this implies a theorem of Costantini on topological completeness of . We show that for nonseparable the hyperspace may contain a closed copy of the rationals. This answers a question of Zsilinszky.