Further note on Fréchet spaces
Hemirings, congruences and the Hewitt realcompactification.
Local extension of maps.
Mazur spaces.
Moscow spaces, Pestov-Tkačenko Problem, and -embeddings
We show that there exists an Abelian topological group such that the operations in cannot be extended to the Dieudonné completion of the space in such a way that becomes a topological subgroup of the topological group . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the...
-абсолют и интегрируемые по Риману функции.
On a theorem of van Douwen.
On a theorem of W.W. Comfort and K.A. Ross
A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group and prove that every -dense subspace of a topological group , such...
On continuous extensions.
On essential ring embeddings and the epimorphic hull of .
On generalizations of Borsuk's homotopy extension theorem
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 some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.
For a completely regular space X, C*(X) denotes the algebra of all bounded real-valued continuous functions over X. We consider the topology of uniform convergence over C*(X).When K is a compact space, the Stone-Weierstrass and Kakutani-Stone theorems provide necessary and sufficient conditions under which a function f ∈ C*(K) can be uniformly approximated by members of an algebra, lattice or vector lattice of C*(K). In this way, the uniform closure and, in particular, the uniform density of algebras...
On some test spaces in dimension theory
Pasting topological spaces at one point
Let be a family of topological spaces and , for every . Suppose is the quotient space of the disjoint union of ’s by identifying ’s as one point . We try to characterize ideals of according to the same ideals of ’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let be an infinite cardinal. (1) Is there any ring and an ideal in such that is an irreducible intersection of prime ideals? (2) Is there...
P-embedding and product spaces
Real-valued functions on Alexandroff (zero-set) spaces
Reflective functors via nearness
Relations between ß X / X and a Certain Subspace of ... X.
Relatively realcompact sets and nearly pseudocompact spaces
A space is said to be nearly pseudocompact iff is dense in . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.