(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 →...

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,...

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

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

space Metacompact space Noetherian topological space Orthocompact space Paracompact space Quasi-compact morphism Precompact set - also called totally bounded...

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

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...

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

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...

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...

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

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

Littlewood subordination theorem Subordinate partition of unity in paracompact space This disambiguation page lists articles associated with the title...

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

Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential space First-countable space Second-countable space...

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...

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...

{C} ;} whose fibers are Ex ⊗R C. Any complex vector bundle over a paracompact space admits a hermitian metric. The basic invariant of a complex vector...

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

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...

refinement. Paracompact A space is paracompact if every open cover has a locally finite open refinement. Paracompact implies metacompact. Paracompact Hausdorff...

every normal metacompact space is a shrinking space. In particular, every Hausdorff paracompact space is a shrinking space. These facts are particularly...

{\displaystyle Y} in Φ {\displaystyle \Phi } is, with the subspace topology, a paracompact space; and has some Z {\displaystyle Z} in Φ {\displaystyle \Phi } which...

mathematical field of general topology, a Dowker space is a topological space that is T4 but not countably paracompact. They are named after Clifford Hugh Dowker...

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

Alexandrov. In fact, this proved the paracompact nature of separable metric spaces (although the term "paracompact space" was introduced by Jean Dieudonné...

_{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...

.} This space is not compact, but the union of any countable set of compact subspaces has compact closure. Some examples of non-paracompact manifolds...