(1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits...

topology is a topological space associated to a vector bundle, over any paracompact space. One way to construct this space is as follows. Let p : E →...

space to be metrizable. Metrizable spaces inherit all topological properties from metric spaces. For example, they are Hausdorff paracompact spaces (and...

the above examples, all paracompact Hausdorff spaces are normal, and all paracompact regular spaces are normal; All paracompact topological manifolds are...

space is said to be a-paracompact if every open cover of the space has a locally finite refinement. In contrast to the definition of paracompactness,...

topological spaces: Every paracompact space is metacompact. This implies that every compact space is metacompact, and every metric space is metacompact...

uniformity on X is complete. Every regular paracompact space (in particular, every Hausdorff paracompact space) is completely uniformizable. (Shirota's...

Minkowski space Müntz space Normed space Paracompact space Perfectoid space Planar space Polish space Probability space Projective space Proximity space Quadratic...

compact sets Lindelöf space Metacompact space Noetherian topological space Orthocompact space Paracompact space Quasi-compact morphism Precompact set -...

finite. Every countably compact paracompact space is compact. More generally, every countably compact metacompact space is compact. Every countably compact...

483-496, 1966. [2] Compact space Paracompact space Normal space Realcompact space Metacompact space Orthocompact space Tychonoff space Engelking, Ryszard (1968)...

classifying space for the unitary group U(n) is a space BU(n) together with a universal bundle EU(n) such that any hermitian bundle on a paracompact space X is...

{\displaystyle K} is complete. Compact space Locally compact space Measure of non-compactness Orthocompact space Paracompact space Relatively compact subspace Sutherland...

property of collections of subsets of a topological space. It is fundamental in the study of paracompactness and topological dimension. Note that the term locally...

regular Lindelöf space is normal. Every regular Lindelöf space is paracompact. A countable union of Lindelöf subspaces of a topological space is Lindelöf....

Hence, we have the following: every metacompact space, and in particular, every paracompact space, is orthocompact. Useful theorems: Orthocompactness...

topological space is also point-finite. A topological space in which every open cover admits a locally finite open refinement is called a paracompact space. Every...

regular topological space (in fact, for a T1-space) to be paracompact. A family E i {\displaystyle E_{i}} of subsets of a topological space is said to be closure-preserving...

Introduction to Metric Spaces and Fixed Point Theory, page 14, John Wiley & Sons Rudin, Mary Ellen. A new proof that metric spaces are paracompact Archived 2016-04-12...

differentiable structure that the topological space supports.) The real line is a locally compact space and a paracompact space, as well as second-countable and normal...

vector bundle of rank n {\displaystyle n} over a paracompact space X {\displaystyle X} . There exists a space Y = F l ( E ) {\displaystyle Y=Fl(E)} , called...

metrizable nor paracompact. Since metrizability is such a desirable property for a topological space, it is common to add paracompactness to the definition...

E_{x}\otimes _{\mathbb {R} }\mathbb {C} } . Any complex vector bundle over a paracompact space admits a hermitian metric. The basic invariant of a complex vector...

following: Michael Selection Theorem—Let X be a paracompact space and Y be a separable Banach space. Let F : X → Y {\displaystyle F\colon X\to Y} be...

hyperbolic space are tessellations of convex uniform polyhedron cells. In 3-dimensional hyperbolic space there are 23 Coxeter group families of paracompact uniform...

to nonregular Hausdorff spaces. There are many situations where another condition of topological spaces (such as paracompactness or local compactness) will...

Hausdorff spaces. There are many situations where another condition of topological spaces (such as normality, pseudonormality, paracompactness, or local...

lifting. If E {\displaystyle E} is a principal G-bundle over a paracompact space, that is, a space with a free and transitive (topological) group action of...

_{n}^{\mathbb {R} }(X)} for any paracompact space X. Since G n {\displaystyle G_{n}} is the direct limit of compact spaces, it is paracompact and so there is a unique...

dimension of a normal space is less than or equal to the large inductive dimension. The covering dimension of a paracompact Hausdorff space X {\displaystyle...