In this article 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.
Orbits and bi-invariant subsets of binary G-spaces are studied. The problem of the distributivity of a binary action of a group G on a space X, which was posed in 2016 by one of the authors, is solved. 2020 Mathematics Subject Classification. 54H15; 57S99. Key words and phrases. binary operation, topological group, groups of homeomorphisms, representations of a topological groups.
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 [9]).
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 interpreted by this the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of the shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is a uniformly movable category. This is a weakened version of the categorical notion of uniform movability introduced by the second author.
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