Examples of disks in /G which cannot be approximated by P-liftable disks
Exemples d'actions non continues d'un groupe dans un compact.
Exotic ANR's via null decompositions of Hilbert cube manifolds
Exponential domination in function spaces
Given a Tychonoff space and an infinite cardinal , we prove that exponential -domination in is equivalent to exponential -cofinality of . On the other hand, exponential -cofinality of is equivalent to exponential -domination in . We show that every exponentially -cofinal space has a -small diagonal; besides, if is -stable, then . In particular, any compact exponentially -cofinal space has weight not exceeding . We also establish that any exponentially -cofinal space with...
Fine topologies as examples of non-Blumberg Baire spaces
Fineness in the category of all 0-dimensional uniform spaces
First countable and countable spaces all compactifications of which contain βN
Four mapping problems of Maćkowiak
In his paper "Continuous mappings on continua" [5], T. Maćkowiak collected results concerning mappings on metric continua. These results are theorems, counterexamples, and unsolved problems and are listed in a series of tables at the ends of chapters. It is the purpose of the present paper to provide solutions (three proofs and one example) to four of those problems.
Function spaces with intervals as domain spaces
Further note on Fréchet spaces
General hedgehogs in general topology
Generalizations of Lašnev's theorem
Group reflection and precompact paratopological groups
We construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups. We also prove that the group reflection of the product of an arbitrary family of paratopological (even semitopological) groups is topologically isomorphic to the product of the group reflections of the factors,...
Homeomorphisms of powers of metric spaces
Inversion in a class of lattice-ordered algebras
Linear subspace of Rl without dense totally disconnected subsets
In [1] the author showed that if there is a cardinal κ such that then there exists a completely regular space without dense 0-dimensional subspaces. This was a solution of a problem of Arkhangel’skiĭ. Recently Arkhangel’skiĭ asked the author whether one can generalize this result by constructing a completely regular space without dense totally disconnected subspaces, and whether such a space can have a structure of a linear space. The purpose of this paper is to show that indeed such a space can...
L-space without any uncountable 0-dimensiolan subspace
Luzin and anti-Luzin almost disjoint families
Under every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.
Metacompactness and the class MOBI
Monotonically normal -separable spaces may not be perfect
A topological space is said to be -separable if has a -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that -separable PIGO spaces are perfect and asked if -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of -separable monotonically normal spaces which are not perfect. Extremely normal -separable spaces are shown to be stratifiable.