Averbukh, Boris G.
Published in
Topological Algebra and its Applications

Using properties of unitary Cauchy filters on monothetic monoids, we prove a criterion of the existence of an embedding of such a monoid into a topological group. The proof of the sufficiency is constructive: under the corresponding assumptions, we are building a dense embedding of a given monothetic monoid into a monothetic group.

Yildirim, Isa Ansari, Arslan Hojat
Published in
Topological Algebra and its Applications

In this paper, we consider, discuss, improve and generalize recent fixed point results for mappings in b-metric space. These results are generalizations of the analogous ones recently proved by Khojasteh et al. [12] and Demma et al. [8].

Gutik, Oleg
Published in
Topological Algebra and its Applications

We describe the structure of Hausdorff locally compact semitopological O-bisimple inverse ω- semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological O-bisimple inverse ω-semigroup with a compact maximal subgroup is either compact or it is a topological sum of its H-classes. We describe the ...

Bardyla, Serhii
Published in
Topological Algebra and its Applications

A topology τ on a monoid S is called shift-continuous if for every a, b ∈ S the two-sided shift S → S, x ↦ axb, is continuous. For every ordinal α ≤ ω, we describe all shift-continuous locally compact Hausdorff topologies on the α-bicyclic monoid Bα. More precisely, we prove that the lattice of shift-continuous locally compact Hausdorff topologies ...

Pastukhova, Iryna
Published in
Topological Algebra and its Applications

We find conditions on topological inverse semigroups X, Y guaranteeing the continuity of any homomorphism h : X → Y having continuous restrictions to any subsemilattice and any subgroup of X.

Banakh, Taras Chervak, Ostap Martynyuk, Tetyana Pylypovych, Maksym Ravsky, Alex Simkiv, Markiyan
Published in
Topological Algebra and its Applications

Generalizing the famous 14-set closure-complement Theorem of Kuratowski from 1922, we prove that for a set X endowed with n pairwise comparable topologies Ʈ1 ⊂ · · · ⊂ Ʈn, by repeated application of the operations of complement and closure in the topologies Ʈ1, . . . , Ʈn to a subset A ⊂ X we can obtain at most

Hušek, Miroslav
Published in
Topological Algebra and its Applications

In [7] a relation between completeness of certain uniformity on ordered sets and restrictions of homeomorphisms of compactifications is described. We shall add more details here and correct one proof.

Artemovych, Orest D. Prykarpatski, Anatolij K. Blackmore, Denis L.
Published in
Topological Algebra and its Applications

We study algebraic properties of Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Special attention is paid to the Poisson brackets of the Lie-Poisson type, related with the special Lie-structures on the differential-topological torus and brane algebras, generalizing those studied before ...

Shlossberg, Menachem
Published in
Topological Algebra and its Applications

In relation to Itzkowitz’s problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced.We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In p...

Karlova, Olena Mykhaylyuk, Volodymyr
Published in
Topological Algebra and its Applications

We prove that if X is a paracompact connected space and Z = ∏s∈S Zs is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map g : X → Z there exists a separately continuous map f : X2 → Z such that f (x, x) = g(x) for all x ∈ X.