- In
topology and
related areas of mathematics, a
metrizable space is a
topological space that is
homeomorphic to a
metric space. That is, a topological...
- In mathematics, a
completely metrizable space (metrically
topologically complete space) is a
topological space (X, T) for
which there exists at
least one...
- In
functional analysis and
related areas of mathematics, a
metrizable (resp. pseudometrizable)
topological vector space (TVS) is a TVS
whose topology is...
-
characterizes when a
topological space is
metrizable. The
theorem states that a
topological space X {\displaystyle X} is
metrizable if and only if it is regular,...
-
discipline of
general topology, a
Polish space is a
separable completely metrizable topological space; that is, a
space homeomorphic to a
complete metric...
- if it is
metrizable with a
separable and
complete metric.
Locally metrizable. A
space is
locally metrizable if
every point has a
metrizable neighbourhood...
- equivalent. Therefore, the
lower limit topology on the real line is not
metrizable. In second-countable spaces—as in
metric spaces—compactness, sequential...
- In mathematics,
topological groups are the
combination of
groups and
topological spaces, i.e. they are
groups and
topological spaces at the same time,...
- {M}}\right)} . A
metrizable space is an AR if and only if it is
contractible and an ANR. By Dugundji,
every locally convex metrizable topological vector...
- (equipped with the
topology induced by the
uniform structure). Any (pseudo)
metrizable space is
uniformizable since the (pseudo)metric
uniformity induces the...
