Abstract:
This article discusses the topological and geometric properties of the set of coupled systems and the properties of its subspaces that are homotopically dense. Theorems for a metrizable nondegenerate continuum are presented, conditions for a homotopically dense set of a compact set and conditions for determining a manifold for a finite-dimensional set depending on the fact that it does not contain a Hilbert cube are determined.
Keywords:subspace, topological properties of a set, geometric properties of a set, topological variety, homotopy dense subspace, metrizable non-degenerate continuum, finite-dimensional set, Hilbert cube.
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