14 citations · 62 across the 18 of their papers we have counts for
18 papers
On the Transitive Binary -Spaces
Pavel S. Gevorgyan
Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are al…
Equivariant Fibrations
Pavel S. Gevorgyan
In this paper, we study equivariant Hurewicz fibrations, obtain their internal characteristics, and prove theorems on relationship between equivariant fibrations and fibrations gen…
Bi-Equivariant Extensions Of Maps
Pavel S. Gevorgyan
The problem of bi-equivariant extension of continuous maps of binary -spaces is considered. The concept of a structural map of distributive binary -spaces is introduced, and…
On transitive and homogeneous binary -spaces
Pavel S. Gevorgyan, Quitzeh Morales Melendez
In this paper, the notions of transitivity and homogeneity in binary -spaces are studied. These notions coincide for distributive binary -spaces. For compact , it is shown…
On Orbit Spaces of Distributive Binary -Spaces
Pavel S. Gevorgyan
The orbit space of a distributive binary -space is studied. A number of its properties in the case of a compact binarily acting group are established.
Strong Movable Categories and Strong Movability of Topological Spaces
Pavel S. Gevorgyan, T. A. Avakyan
The paper is devoted to one of the important notions of the shape theory: that of strong movability, which was primarily introduced by K. Borsuk for metrizable compacts. A strong m…
Uniformly Movable Categories And Uniform Movability Of Topological Spaces
Pavel S. Gevorgyan, I. Pop
A categorical generalization of the notion of movability from the inverse systems and shape theory was given by the first author who defined the notion of movable category and inte…
On equivariant fibrations of -CW-complexes
Pavel S. Gevorgyan, Rolando Jimenez
It is proved that if is a compact Lie group, then an equivariant Serre fibration of -CW-complexes is an equivariant Hurewicz fibration in the class of compactly generated $G…
Equivariant Movability of Topological Groups
Pavel S. Gevorgyan
The equivariant movability of topological spaces with an action of a given topological group is considered. In particular, the equivariant movability of topological groups is s…
Groups of Invertible Binary Operations of a Topological Space
Pavel S. Gevorgyan
In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible…
Yu. M. Smirnov's General Equivariant Shape Theory
Pavel S. Gevorgyan
A general equivariant shape theory for arbitrary -spaces in the case of a compact group is constructed by using the method of pseudometrics suggested by Yu. M. Smirnov as ea…
Shape Theory
Pavel S. Gevorgyan
Shape theory was founded by K.~Borsuk 50 years ago. In essence, this is spectral homotopy theory; it occupies an important place in geometric topology. The article presents the bas…
Bi-Equivariant Fibrations
Pavel S. Gevorgyan
The lifting problem for continuous bi-equivariant maps and bi-equivariant covering homotopies is considered, which leads to the notion of a bi-equivariant fibration. An intrinsic c…
On Orbits and Bi-invariant Subsets of Binary -Spaces
Pavel S. Gevorgyan, A. A. Nazaryan
Orbits and bi-invariant subsets of binary -spaces are studied. The problem of the distributivity of a binary action of a group on a space , which was posed in 2016 by one…
Groups of Binary Operations and Binary -Spaces
Pavel S. Gevorgyan
The group of continuous binary operations on a topological space is studied; its relationship with the group of homeomorphisms is established. The category of binary -spaces and…
Movability and co-movability of shape morphisms
P. S. Gevorgyan, I. Pop
The purpose of this paper is to define some notions of movability for morphisms of inverse systems which extend the movability properties of inverse systems and which are compatibl…
Some questions of equivariant movability
Pavel S. Gevorgyan
In this paper the some questions of equivariant movability connected with substitution of acting group on closed subgroup and with transitions to spaces of -orbits and $…
Movable categories
Pavel S. Gevorgyan
The notion of movability for metrizable compacts was introduced by K.Borsuk. In this paper we define the notion of movable category and prove that the movability of a topological s…