Construction of infinite-dimensional relative homotopy groups in Hilbert space (Q1397535)

The article is related to some important problems of infinite-dimensional algebraic topology, particularly, to the construction of infinite-dimensional relative homotopy groups of pointed pairs of subsets of a real Hilbert space \(H\). In the article, a rather narrow class of admissible mappings is considered. The author follows the ideas of Leray, Schauder, V. G. Boltyanskii and constructs an admissible class \(K\) of continuous mappings of subsets of a real Hilbert space, which may be used for construction of the infinite-dimensional algebraic topology in the Hilbert space. The author together with V. G. Boltyanskii previously showed that the ideas of Leray and Schauder allowed them to extend the concept of mapping degree to a certain subclass of the class \(K_0\). To accomplish this, the author takes as a basis class \(K_0\) and constructs infinite-dimensional homotopy groups of two types (compact and noncompact) of subsets of a separable Hilbert space.