Definition:Topologically Complete Space

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This page is about Topologically Complete Space. For other uses, see Complete.

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $M = \struct {S, d}$ be a complete metric space such that $\struct {S, \tau}$ is the topological space induced by $d$.


If there exists such a complete metric space, then $T$ is described as topologically complete.


Also see

  • Results about Topologically Complete Spaces can be found here.


Sources