On Generating Quasi Uniformities.
On groups of essential values of topological cylinder cocycles over minimal rotations
A theory of essential values of cocycles over minimal rotations with values in locally compact Abelian groups, especially , is developed. Criteria for such a cocycle to be conservative are given. The group of essential values of a cocycle is described.
On -bubbles in n-dimensional compacta
A topological space X is called an -bubble (n is a natural number, is Čech cohomology with integer coefficients) if its n-dimensional cohomology is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any -bubbles; and (3) Every n-acyclic finite-dimensional -trivial metrizable compactum...
On H. Priestley's dual of the category of bounded distributive lattices
On half-completion and bicompletion of quasi-metric spaces
We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space is quasi-metric if and only if is finite.
On Hamel bases in Banach spaces
It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.
On Hattori spaces
For a subset of the real line , Hattori space is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on which are sufficient and necessary for to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in...
On Hausdorff compactifications of non-locally compact spaces.
On Hausdorff dimension of random fractals.
On Hausdorff intrinsic metric.
On Hausdorff Quotients of Spaces and Magill's Theorem.
On Hausdorffness and compactness in intuitionistic fuzzy topological spaces
On hedgehog-topologically fine uniform spaces
On hereditarily decomposable hereditarily equivalent non-metric continua
On hereditarily indecomposable compacta
On hereditarily normal topological groups
We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under...
On hereditarily separable Hausdorff spaces in the constructible universe
On hereditarily α-Lindelöf and α-separable spaces, II
On hereditary and product-stable quotient maps
It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.
On hereditary interval algebras.