11. Property preservation and invariance

Preservations and invariances of topological properties (separateness, countability, compactness and connectedness) of topological spaces are covered in [AF97] and naturally apply to metric spaces.

11.1 Bornitude

A uniformly continuous application preserves bornitude (p. 162 of

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Bibliography

(1) - AARTS (J.M.), NISHIURA (T.) - Dimension and Extensions, - North Holland, 331 pages (1993).
(2) - ADAMS (C.), FRANZOSA (R.) - Introduction to Topology Pure and Applied, - Pearson, 507 pages (2008).
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