precompact set

precompact set

[prē′käm‚pakt ‚set]
(mathematics)
A set in a metric space which can always be covered by open balls of any diameter about some finite number of its points. Also known as totally bounded set.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Suppose that a semiflow on [bar.[OMEGA]] leaves both [OMEGA] and [partial derivative][OMEGA] forward invariant, maps bounded sets in [bar.[OMEGA]] to precompact set for t > 0, and it is dissipative.
Saadati and Park [13] defined precompact set in intuitionistic fuzzy metric spaces and proved that any subset of an intuitionistic fuzzy metric space is compact if and only if it is pre-compact and complete.
Kakol, "On precompact sets in spaces [C.sub.c] (X)," Georgian Mathematical Journal, vol.
Cobzas, Compact and precompact sets in asymmetric locally convex spaces, Topology Appl.