Examples of 'hausdorff spaces' in a sentence
Meaning of "hausdorff spaces"
hausdorff spaces - Hausdorff spaces are types of topological spaces in mathematics that satisfy a separation axiom known as the Hausdorff condition. These spaces are named after the German mathematician Felix Hausdorff and play a significant role in various areas of mathematics, such as topology and analysis
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- plural of Hausdorff space
How to use "hausdorff spaces" in a sentence
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hausdorff spaces
We also characterize the locally compact hausdorff spaces which are paracompact.
Hausdorff spaces are topological spaces in which individual points have disjoint neighborhoods.
Compact subspaces of Hausdorff spaces are closed.
In the following we will assume all groups are Hausdorff spaces.
There exist Hausdorff spaces that are not regular.
These are what we usually call normal Hausdorff spaces.
Embeddings into compact Hausdorff spaces may be of particular interest.
Soft sheaves are acyclic over paracompact Hausdorff spaces.
Another nice property of Hausdorff spaces is that compact sets are always closed.
The situation is different for countably infinite compact Hausdorff spaces.
Quotient spaces of locally compact Hausdorff spaces are compactly generated.
Tychonoff spaces are precisely those spaces which can be embedded in compact Hausdorff spaces.
Compact Hausdorff spaces are normal.
It is widely applicable since all metric spaces and all compact Hausdorff spaces are normal.
Paracompact Hausdorff spaces are regular.
See also
Similarly locally compact Tychonoff spaces are usually just referred to as locally compact Hausdorff spaces.
Normal Hausdorff spaces are always Tychonoff.
Such functions exist by the Tietze extension theorem which applies to locally compact Hausdorff spaces.
Every product of Hausdorff spaces is Hausdorff.
There are many results for topological spaces that hold for both regular and Hausdorff spaces.
Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology.
Urysohn and completely Hausdorff spaces.
HComp, compact Hausdorff spaces and continuous functions.
Extremally disconnected Hausdorff spaces.
The concept of a Hilbert-Schmidt operator may be extended to any locally compact Hausdorff spaces.
However, often topological spaces must be Hausdorff spaces where limit points are unique.
Hence, the specialization order is of little interest for T1 topologies, especially for all Hausdorff spaces.
Separated spaces are also called Hausdorff spaces or T2 spaces.
In fact, this property characterizes the compact Hausdorff spaces.
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Examples of using Spaces
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The interior spaces are rich and varied
Spaces and digits take first priority
But let there be spaces in your togetherness
Examples of using Hausdorff
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About fractals not needing a hausdorff dimension
Hausdorff separation axiom
We also characterize the locally compact hausdorff spaces which are paracompact
