A note on maximally resolvable spaces.
A note on splittable spaces
A space is splittable over a space (or splits over ) if for every there exists a continuous map with . We prove that any -dimensional polyhedron splits over but not necessarily over . It is established that if a metrizable compact splits over , then . An example of -dimensional compact space which does not split over is given.
A note on topological groups and their remainders
In this note we first give a summary that on property of a remainder of a non-locally compact topological group in a compactification makes the remainder and the topological group all separable and metrizable. If a non-locally compact topological group has a compactification such that the remainder of belongs to , then and are separable and metrizable, where is a class of spaces which satisfies the following conditions: (1) if , then every compact subset of the space is a...
A Note On Ultrapower Cardinality
A note on ultrapower cardinality.
A note on zero-dimensional preimages of compact spaces
A note on -universal spaces
A pseudocompact space with Kelley's property has a strictly positive measure
A Remark On Filter Regularity
A remark on filter regularity.
A remark on the Moore theorem.
A remark on the tightness of products
We observe the existence of a -compact, separable topological group and a countable topological group such that the tightness of is countable, but the tightness of is equal to .
A sufficient condition for maximal resolvability of topological spaces
We show a new theorem which is a sufficient condition for maximal resolvability of a topological space. We also discuss some relationships between various theorems about maximal resolvability.
A topological characterization of stationary sets
A weakening of , with applications to topology
AB-compacta
Abelian torsion groups with a pseudocompact group topology.
About remainders in compactifications of homogeneous spaces
We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space , every remainder of is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.
Absolute points in
Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom