Examples of 'compact hausdorff' in a sentence
Meaning of "compact hausdorff"
In mathematics, this phrase is used to describe a topological space that satisfies both the compactness and Hausdorff properties. It is commonly used in the context of general topology
How to use "compact hausdorff" in a sentence
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compact hausdorff
We also characterize the locally compact hausdorff spaces which are paracompact.
Tychonoff spaces are precisely those spaces which can be embedded in compact Hausdorff spaces.
A locally compact Hausdorff space is always locally normal.
The situation is different for countably infinite compact Hausdorff spaces.
Embeddings into compact Hausdorff spaces may be of particular interest.
It is widely applicable since all metric spaces and all compact Hausdorff spaces are normal.
Every ultrafilter on a compact Hausdorff space converges to exactly one point.
Similarly locally compact Tychonoff spaces are usually just referred to as locally compact Hausdorff spaces.
Every discrete subgroup of a compact Hausdorff group is finite.
Compact Hausdorff spaces are normal.
Quotient spaces of locally compact Hausdorff spaces are compactly generated.
Such functions exist by the Tietze extension theorem which applies to locally compact Hausdorff spaces.
The Tychonoff plank is a compact Hausdorff space and is therefore a normal space.
In fact, this property characterizes the compact Hausdorff spaces.
Every locally compact Hausdorff space is a Baire space.
See also
Conversely, every compactly generated Hausdorff space is a quotient of some locally compact Hausdorff space.
The space of continuous functions on a compact Hausdorff space has a particular importance.
How do the compact Hausdorff topologies sit in the lattice of all topologies on a set?
Closed and open subsets of locally compact Hausdorff space are locally compact.
The concept of a Hilbert-Schmidt operator may be extended to any locally compact Hausdorff spaces.
It follows that every locally compact Hausdorff space is a Tychonoff space.
This result gives a far-reaching generalization of Pontryagin duality for locally compact Hausdorff abelian groups.
Every locally compact Hausdorff space is Tychonoff.
In particular, suppose X is a compact Hausdorff space.
A locally compact Hausdorff space is regular, hence locally regular.
Every perfect, locally compact Hausdorff space is uncountable.
For example, a compact Hausdorff space is metrizable if and only if it is second-countable.
Properties = = The Tychonoff plank is a compact Hausdorff space and is therefore a normal space.
However, a locally compact Hausdorff space is zero-dimensional if and only if it is totally disconnected.
Let X be a locally compact Hausdorff space with a countable base.
Being locally compact Hausdorff spaces, manifolds are necessarily Tychonoff spaces.
Every Tychonoff cube is compact Hausdorff as a consequence of Tychonoff 's theorem.
HComp, compact Hausdorff spaces and continuous functions.
Locally compact Hausdorff space.
A locally compact Hausdorff group is called amenable if it admits a left - ( or right - ) invariant mean.
Theorem 1 Every locally compact Hausdorff topological vector space is finite-dimensional.
Thus, every compact Hausdorff space is H-closed.
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We also characterize the locally compact hausdorff spaces which are paracompact
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