- of the
ambient space). The term
precompact (or pre-compact) is
sometimes used with the same meaning, but
precompact is also used to mean
relatively compact...
-
Precompact set may
refer to:
Relatively compact subspace, a
subset whose closure is
compact Totally bounded set, a
subset that can be
covered by finitely...
- mathematics, a
relatively compact subspace (or
relatively compact subset, or
precompact subset) Y of a
topological space X is a
subset whose closure is compact...
- are equivalent: S {\displaystyle S} is compact, S {\displaystyle S} is
precompact and complete. The
above follows directly from Jean Dieudonné, theorem...
- K\subseteq X'} has
compact closure in the
topology of
uniform convergence on
precompact sets. Furthermore, this
topology on K {\displaystyle K}
coincides with...
- In the
mathematical field of
metric geometry,
Mikhael Gromov proved a
fundamental compactness theorem for
sequences of
metric spaces. In the
special case...
-
subsets are
weakly precompact by Alaoglu's theorem. Thus the
theorem implies that
bounded subsets are
weakly sequentially precompact, and
therefore from...
- In a
Hausdorff locally convex TVS, the
convex hull of a
precompact set is
again precompact. Consequently, in a
complete Hausdorff locally convex space...
-
topological space Orthocompact space Paracompact space Quasi-compact
morphism Precompact set - also
called totally bounded Relatively compact subspace Totally...
- } The weak
maximum principle, in this setting, says that for any open
precompact subset M of the
domain of u, the
maximum of u on the
closure of M is achieved...
