paracompact space

(redirected from Paracompact)

paracompact space

[¦par·ə¦käm‚pakt ‚spās]
(mathematics)
A topological space with the property that every open covering F is associated with a locally finite open covering G, such that every element of G is a subset of an element F.
References in periodicals archive ?
All manifolds considered are smooth, connected, oriented, and paracompact (hence also second-countable).
Theorem A.[17, Theorem 1.2] Let X be a paracompact free [Z.sub.p]-space of ind X [greater than or equal to] n, and f : X [right arrow] M a continuous mapping ofX into an m-dimensional connected manifold M (orientable ifp> 2).
X is an open continuous image of a paracompact Cech-complete space.
Consequently, it is a locally compact countable at infinity space and a paracompact space, which admits the partition of unity by smooth real functions.
with B paracompact, we prove in Theorem 5.6 that these maps have indeed local lifts to PU(H).
Also we attempted to achieve a general form of the well known Michaels theorem on regular paracompact spaces perticularly for [theta]-open sets.
Since [0, T] x [??] is paracompact, there exists a locally finite refinement {[V.sup.k.sub.j]} of this covering.
Ramadan, 1991, On pairwise paracompact spaces, Proc.
I thought to a multi-space also: fragments (potsherds) of spaces put together, say as an example: Banach, Hausdorff, Tikhonov, compact, paracompact, Fock symmetric, Fock antisymmetric, path-connected, simply connected, discrete metric, indiscrete pseudo-metric, etc.
Let [pi]: E [right arrow] N be a vector bundle of (paracompact) base [N.sup.n] and fibre [R.sup.k].
If X is, for example, a connected locally compact, paracompact, and not compact manifold, equipped with a Radon measure p such that [mu](X) = +[infinity], any exhaustive sequence K = [([K.sub.n]).sub.n[member of]N] of compact subsets of X is such that K [member of] [Ren.sub.[mu]].