- (1944).
Every compact space is
paracompact.
Every paracompact Hausdorff space is normal, and a
Hausdorff space is
paracompact if and only if it
admits partitions...
- compact, or even Lindelöf. The (non-extended) long line or ray is not
paracompact. It is path-connected,
locally path-connected and
simply connected but...
-
topological manifolds. In particular, many
authors define them to be
paracompact or second-countable. In the
remainder of this
article a
manifold will...
- said to be a-
paracompact if
every open
cover of the
space has a
locally finite refinement. In
contrast to the
definition of
paracompactness, the refinement...
- the
above examples, all
paracompact Hausdorff spaces are normal, and all
paracompact regular spaces are normal; All
paracompact topological manifolds are...
-
topology is a
topological space ****ociated to a
vector bundle, over any
paracompact space. One way to
construct this
space is as follows. Let p : E → B {\displaystyle...
- 3-dimensional
hyperbolic space there are 23
Coxeter group families of
paracompact uniform honeycombs,
generated as
Wythoff constructions, and represented...
-
topological properties from
metric spaces. For example, they are
Hausdorff paracompact spaces (and
hence normal and Tychonoff) and first-countable. However...
-
functions over a
smooth (
paracompact Hausdorff) manifold, or
modules over
these sheaves of rings. Also, fine
sheaves over
paracompact Hausdorff spaces are...
- a
countable subcover.
Paracompact. A
space is
paracompact if
every open
cover has an open
locally finite refinement.
Paracompact Hausdorff spaces are normal...
