- 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...
- \Rightarrow } 2 holds,
since in
particular any
properly metrisable space is
countable union of
compact metrisable and thus
separable (cf.
properties of compact...
-
consisting of
clopen sets. The
three notions above agree for separable,
metrisable spaces.[citation needed][clarification needed] A zero-dimensional Hausdorff...
- logic.
Marczewski proved that the
topological dimension, for
arbitrary metrisable separable space X,
coincides with the
Hausdorff dimension under one of...
- In mathematics, a
completely metrizable space (metrically
topologically complete space) is a
topological space (X, T) for
which there exists at
least one...
-
being normal.
Every locally compact group which is first-countable is
metrisable as a
topological group (i.e. can be
given a left-invariant
metric compatible...
- if
every Cauchy sequence converges.
Completely metrizable/completely
metrisable See
complete space.
Completely normal A
space is
completely normal if...
-
emphasis on
applications to non-
metrisable manifolds and
topological properties of
manifolds close to
metrisability.
Gauld has aut****d two monographs...
- is a
uniform space (such as any
metric space or any
topological group,
metrisable or not),
there is the
topology of
compact convergence on the set F ( X...
-
measures on X {\displaystyle X} is tight. This is not
necessarily so for non-
metrisable compact spaces. If we take [ 0 , ω 1 ] {\displaystyle [0,\omega _{1}]}...
