Normality and paracompactness in subsets of product spaces
Normality and paracompactness of Pixley-Roy hyperspaces
Note on category in Cartesian products of metrizable spaces
Note on decompositions of metrizable spaces I
Note on decompositions of metrizable spaces II
Note on extremal points
Note on metrization of quasi-uniform spaces
O množinách vzdialeností množín metrického priestoru
On a certain lattice of topologies on a product of metric spaces
On a class of topological spaces with a Scott sentence
On a functional inequality arising in the construction of the product of several metric spaces.
On a metrization of the hyperspace of a metric space
On a problem of J. Nagata
On a problem of Sikorski
On a product of metric spaces
On a property of pseudometrics and uniformities near to convexity
On a shadowing lemma in metric spaces
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map , where is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map .
On a weak form of uniform convergence
The notion of -convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on implies -convergence are -compact spaces. We show that the assumption...
On Asymmetric Distances
In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the...
On butterfly-points in , Tychonoff products and weak Lindelöf numbers
Let be the Tychonoff product of -many Tychonoff non-single point spaces . Let be a point in the closure of some whose weak Lindelöf number is strictly less than the cofinality of . Then we show that is not normal. Under some additional assumptions, is a butterfly-point in . In particular, this is true if either or and is infinite and not countably cofinal.