Some questions of equivariant movability

In this paper the some questions of equivariant movability connected with substitution of acting group $G$ on closed subgroup $H$ and with transitions to spaces of $H$-orbits and $H$-fixed points spaces are investigated. In the special case the characterization of equivariant-movable $G$-spaces is given.Comment: 12 page

Movable categories

The notion of movability for metrizable compacts was introduced by K.Borsuk $[1]$. In this paper we define the notion of movable category and prove that the movability of a topological space $X$ coincides with the movability of a suitable category, which is generated by the topological space $X$ (i.e., the category $W^X$, defined by S.Mardesic)

Some questions of equivariant movability

In this article some questions of equivariant movability, connected with the substitution of the acting group G on closed subgroup H and with transitions to spaces of H-orbits and H-fixed points spaces, are investigated. In a special case, the characterization of equivariantly movable G-spaces is given

Shape Theory

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 basic concepts and the most important, in our opinion, results of shape theory. Unfortunately, many other interesting problems and results related to this theory could not be covered because of space limitations. The article contains an extensive bibliography for those who wants to gain a more detailed and systematic insight into the issues considered in the survey.Comment: 46 page

Movable categories

The notion of movability for metrizable compacta was introduced by K.Borsuk. In this paper we define the notion of a movable category and prove that the movability of a topological space X coincides with the movability of a suitable category, which is generated by the topological space X (i.e., the category X, defined by S.Mardesic)

Bi-Equivariant Fibrations

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 characteristic of a bi-equivariant Hurewicz fibration is obtained. Theorems concerning a relationship between bi-equivariant fibrations and fibrations generated by them are proved.Comment: 8 page

Yu. M. Smirnov's General Equivariant Shape Theory

A general equivariant shape theory for arbitrary $G$-spaces in the case of a compact group $G$ is constructed by using the method of pseudometrics suggested by Yu. M. Smirnov as early as in 1985 at the fifth Tiraspol symposium on general topology and its applications.Comment: 8 page