On one generalization of weakly compactly generated Banach spaces
On one-parameter families of diffeomorphisms. II: Generic branching in higher dimensions
On one-point -compactification and local - compactness
On open light mappings
Whyburn has proved that each open mapping defined on arc (a simple closed curve) is light. Charatonik and Omiljanowski have proved that each open mapping defined on a local dendrite is light. Theorem 3.8 is an extension of these results.
On open maps and related functions over the Salbany compactification
Given a topological space , let and denote, respectively, the Salbany compactification of and the compactification map called the Salbany map of . For every continuous function , there is a continuous function , called the Salbany lift of , satisfying . If a continuous function has a stably compact codomain , then there is a Salbany extension of , not necessarily unique, such that . In this paper, we give a condition on a space such that its Salbany map is open. In particular,...
On open maps of Borel sets
We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.
On Optimal Realizations of Finite Metric Spaces by Graphs.
On order locally finite and closure-preserving covers
On order topology of spaces having uniform linearly ordered bases
On orderability of topological groups.
On ordered topological spaces
On oriented metric spaces
On oscillation of limit functions.
On -paracompact spaces.
On -closed spaces.
On -sequential -compact spaces
It is shown that a space is -Weakly Fréchet-Urysohn for iff it is -Weakly Fréchet-Urysohn for arbitrary , where is the -th left power of and for . We also prove that for -compact spaces, -sequentiality and the property of being a -Weakly Fréchet-Urysohn space with , are equivalent; consequently if is -compact and , then is -sequential iff is -sequential (Boldjiev and Malyhin gave, for each -point , an example of a compact space which is -Fréchet-Urysohn and it is...
On and weakly- spaces.
On pairs of compacta with dim(X×Y) < dimX + dimY
On Pairwise Lindelöf Spaces.
On pairwise S-closed bitopological spaces.