Homogeneity of βG if G is a topological group
Homomorphic images of -factorizable groups
It is well known that every -factorizable group is -narrow, but not vice versa. One of the main problems regarding -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every -narrow group is a continuous homomorphic image of an -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an -factorizable...
Homotopically labile points of locally compact metric spaces
How sensitive is to changes in and/or ?
We investigate how the Lindelöf property of the function space is influenced by slight changes in and/or .
Hurewicz properties, non distinguishing convergence properties and sequence selection properties
Hyperspace of the approximate inverse limit
Hyperspace selections avoiding points
We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic...
Hyperspaces of noncompact metric spaces
-Lindelöf spaces.
Ideal equivalences for almost real-compact spaces
Ideals of the Stone-Cech compactification of semigroups.
Ideals of uniformly continuous mappings on pseudometric spaces
Identifying and distinguishing various varieties of abelian topological groups [Book]
In a left-topological semigroup with dense center the closure of any left ideal is an ideal.
In quest of weaker connected topologies
We study when a topological space has a weaker connected topology. Various sufficient and necessary conditions are given for a space to have a weaker Hausdorff or regular connected topology. It is proved that the property of a space of having a weaker Tychonoff topology is preserved by any of the free topological group functors. Examples are given for non-preservation of this property by “nice” continuous mappings. The requirement that a space have a weaker Tychonoff connected topology is rather...
In search for Lindelöf ’s
It is shown that if is a first-countable countably compact subspace of ordinals then is Lindelöf. This result is used to construct an example of a countably compact space such that the extent of is less than the Lindelöf number of . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.
Induced measures on Wallman spaces.
Inductive compactness as a generalization of semicompactness
Inductive dimensions for completely regular spaces
Infinite probabilistic secret sharing
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of participants allows us to investigate their abstract properties, to connect the topic to other branches of mathematics, and to discover new design paradigms. A scheme is perfect if unqualified subsets have no information on the secret, that is, their total share...