On homotopically dense subspaces of the space of complete linked systems

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.

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