Examples of 'paracompact' in a sentence
Meaning of "paracompact"
Paracompact is an adjective used in mathematics to describe a topological space in which every open cover has an open locally finite refinement
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- In which every open cover admits an open locally finite refinement.
How to use "paracompact" in a sentence
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paracompact
A product of paracompact spaces need not be paracompact.
A new proof that metric spaces are paracompact.
It is called paracompact because it has infinite cells.
It is an example of a metacompact space that is not paracompact.
Every closed subspace of a paracompact space is paracompact.
A manifold is metrizable if and only if it is paracompact.
Every feebly compact paracompact space is compact.
Every shrinking space is countably paracompact.
A paracompact space is collectionwise normal.
Every metric space is paracompact.
Every paracompact space is metacompact.
Every compact space is paracompact.
Paracompact manifolds have all the topological properties of metric spaces.
This is equivalent to requiring that every open subspace be paracompact.
Paracompact implies metacompact.
See also
Every discrete space is paracompact.
A space is paracompact if every open cover has an open locally finite refinement.
All you never wanted to know about paracompact spaces.
Paracompact topological spaces are spaces for which every open cover contains a locally finite open refinement.
We also characterize the locally compact hausdorff spaces which are paracompact.
A space such that every subspace of it is a paracompact space is called hereditarily paracompact.
It follows that every such space is completely normal as well as paracompact.
Sometimes paracompact spaces are defined so as to always be Hausdorff.
A topological space in which every open cover admits a locally finite open refinement is called paracompact.
Every paracompact differentiable manifold admits a Riemannian metric.
Compact spaces are always Lindelöf and paracompact.
Every paracompact Hausdorff space is normal.
Soft sheaves are acyclic over paracompact Hausdorff spaces.
Paracompact ccc spaces are Lindelöf.
Every regular Lindelöf space is paracompact.
Paracompact Hausdorff spaces are regular.
CW complexes are paracompact.
Let M be a paracompact differentiable manifold.
In particular, a manifold is metrizable if and only if it is paracompact.
In particular, every paracompact space is a shrinking space.
Every compact manifold is second-countable and paracompact.
The category of paracompact spaces paracompact . space.
Every second-countable manifold is separable and paracompact.
In particular, a connected manifold is paracompact if and only if it is second-countable.
At first, we look at some classical characteriztion theorems of paracompact spaces.
Every paracompact space is metacompact, and every metacompact space is orthocompact.
Moreover, if a manifold is separable and paracompact then it is also second-countable.
In particular, every regular Lindelöf space is paracompact.
There are no regular compact or paracompact tessellations of hyperbolic space of dimension 6 or higher.
Paracompact Coxeter groups of rank 3 exist as limits to the compact ones.
This space is Hausdorff, paracompact and first countable.
There are two classes of hyperbolic Coxeter groups, compact and paracompact.
However, the product of a paracompact space and a compact space is always paracompact.
But by the Morita theorem, every regular Lindelöf space is paracompact.
Every metric space is paracompact and Hausdorff, and thus normal.
