- a
similarity between the
definitions of
compactness and
paracompactness: For
paracompactness, "subcover" is
replaced by "open refinement" and "finite"...
- 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...
- 2^{\aleph _{1}}}
isomorphism classes of non-
paracompact surfaces, even when a
generalization of
paracompactness, ω-boundedness, is ****umed.
There are no...
-
product of
paracompact spaces". Bull. Amer. Math. Soc. 53 (6): 631–632. doi:10.1090/S0002-9904-1947-08858-3. Stone, A. H. (1948). "
Paracompactness and product...
- 3-dimensional
hyperbolic space there are 23
Coxeter group families of
paracompact uniform honeycombs,
generated as
Wythoff constructions, and represented...
-
topological space, it is
common to add
paracompactness to the
definition of a manifold. In any case, non-
paracompact manifolds are
generally regarded as...
- {R} ^{n}} . This
extends to any
smooth manifold as a
corollary of
paracompactness. In
differential geometry, zero sets are
frequently used to define...
-
situations where another condition of
topological spaces (such as
paracompactness or
local compactness) will
imply regularity if
preregularity is satisfied...
-
topological properties from
metric spaces. For example, they are
Hausdorff paracompact spaces (and
hence normal and Tychonoff) and first-countable. However...
- and D n {\displaystyle \mathrm {D} _{n}}
demihypercubic families. For
paracompact hyperbolic honeycombs,
there are
three groups in
dimensions 6 and 9,...
