- 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...
-
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...
- 2^{\aleph _{1}}}
isomorphism classes of non-
paracompact surfaces, even when a
generalization of
paracompactness, ω-boundedness, is ****umed.
There are no...
- target: CITEREFEngelking1989 (help)
Ernest Michael,
Another note on
paracompactness, 1957 A. Mathew’s blog post
Ryszard Engelking,
General Topology, Revised...
- 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...
-
situations where another condition of
topological spaces (such as
paracompactness or
local compactness) will
imply regularity if
preregularity is satisfied...
-
uniform space. It is also
useful for
stating a
characterization of
paracompactness. The
general definition makes sense for
arbitrary coverings and does...
- {R} ^{n}} . This
extends to any
smooth manifold as a
corollary of
paracompactness. In
differential geometry, zero sets are
frequently used to define...
