Examples of 'hausdorff space' in a sentence
Meaning of "hausdorff space"
In mathematics, a topological space that satisfies certain separation axioms, named after Felix Hausdorff
Show more definitions
- A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that x∈U and y∈V.
How to use "hausdorff space" in a sentence
Basic
Advanced
hausdorff space
Collectionwise hausdorff space.
Further discussion of separated spaces may be found in the article Hausdorff space.
A locally compact Hausdorff space is always locally normal.
Willard calls this a completely Hausdorff space.
A locally convex Hausdorff space is nuclear if and only if its completion is nuclear.
This can never happen for a Hausdorff space.
The only Hausdorff space that has a generic point is the singleton set.
A compact subspace of a Hausdorff space is closed.
If X is a Hausdorff space then limits of sequences are unique where they exist.
We now show that each finite subset of a Hausdorff space is closed.
A perfectly normal Hausdorff space must also be completely normal Hausdorff.
A topological manifold is a locally Euclidean Hausdorff space.
Every ultrafilter on a compact Hausdorff space converges to exactly one point.
The order topology makes S into a completely normal Hausdorff space.
The Tychonoff plank is a compact Hausdorff space and is therefore a normal space.
See also
In geometry and topology, it is a usual axiom of a manifold to be a Hausdorff space.
Every locally compact Hausdorff space is a Baire space.
Continuum A space is called a continuum if it a compact, connected Hausdorff space.
Every paracompact Hausdorff space is normal.
It is a so-called Kolmogorov space, but it is neither a Fréchet space nor a Hausdorff space.
The space of continuous functions on a compact Hausdorff space has a particular importance.
Every normal Hausdorff space is both Tychonoff and normal regular.
Closed and open subsets of locally compact Hausdorff space are locally compact.
For example, a compact Hausdorff space is metrizable if and only if it is second-countable.
Every pospace is a Hausdorff space.
It can be shown any Hausdorff space which is path-connected is also arc-connected.
The Toronto space problem asks for an uncountable Toronto Hausdorff space that is not discrete.
A locally compact Hausdorff space is regular, hence locally regular.
Extremally disconnected Hausdorff space.
However, a locally compact Hausdorff space is zero-dimensional if and only if it is totally disconnected.
Compactly generated Hausdorff space.
A T3 space or regular Hausdorff space is a topological space that is both regular and a Hausdorff space.
Every continuous map from a compact space to a Hausdorff space is both proper and closed.
A normal Hausdorff space is also called a T4 space.
It follows that every locally compact Hausdorff space is a Tychonoff space.
In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space.
Every completely normal Hausdorff space is also normal Hausdorff.
In particular, any continuous function from a hyperconnected space to a Hausdorff space must be constant.
Regular Hausdorff space.
Every normal regular space is completely regular, and every normal Hausdorff space is Tychonoff.
Every completely Hausdorff space is Urysohn.
In particular, suppose X is a compact Hausdorff space.
It follows that every completely Hausdorff space is Urysohn and every Urysohn space is Hausdorff.
Any Baire probability measure on any locally compact σ-compact Hausdorff space is a regular measure.
It is a completely regular Hausdorff space ( also called Tychonoff space ) that is not normal.
In particular, it is not a Hausdorff space.
In fact, a regular Hausdorff space satisfies the slightly stronger condition T2 ½.
Completely normal Hausdorff space.
Any Hausdorff space must be sober, and any sober space must be T0.
Every locally compact Hausdorff space is Tychonoff.
You'll also be interested in:
Examples of using Hausdorff
Show more
About fractals not needing a hausdorff dimension
Hausdorff separation axiom
We also characterize the locally compact hausdorff spaces which are paracompact
Examples of using Space
Show more
The same space has a cooker hood
I waited five years for that space
The race for space at the table
