Homotopic invariance of infinite-dimensional homotopic groups of Hilbert space subsets

The paper discusses some equivalent ways of construction of infinite-dimensional homotopic groups of subsets and pairs of subsets in real Hilbert spaces. In the admissible class of K ₀-continuous mappings, the homotopic invariance of the mentioned groups and their isomorphism are demonstrated in the case where the basic points belong to the same component of K ₀-linear connectivity.