-
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...
- 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...
- 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...
- net in X
converges (i.e. has a
limit point in X).
Totally bounded (or
Precompact). A
uniform space X is
totally bounded if for each
entourage E ⊂ X × X...
- In a
Hausdorff locally convex TVS, the
convex hull of a
precompact set is
again precompact. Consequently, in a
complete Hausdorff locally convex space...
-
subsets are
weakly precompact by Alaoglu's theorem. Thus the
theorem implies that
bounded subsets are
weakly sequentially precompact, and
therefore from...
-
topological space Orthocompact space Paracompact space Quasi-compact
morphism Precompact set - also
called totally bounded Relatively compact subspace Totally...
- {\displaystyle X} ; (2) the
topology of
pointwise convergence; (3) the
topology of
precompact convergence. By
letting G {\displaystyle {\mathcal {G}}} be the set of...
