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'Alexandrov one-point compactification'
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| Title of object: |
Alexandrov one-point compactification |
| Canonical Name: |
AlexandrovOnePointCompactification |
| Type: |
Definition |
| Created on: |
2003-07-27 10:29:03 |
| Modified on: |
2003-07-27 10:34:37 |
| Classification: |
msc:54D35 |
| Keywords: |
compactification |
| Synonyms: |
Alexandrov one-point compactification=one-point compactification
Alexandrov one-point compactification=Alexandroff one-point compactification
Alexandrov one-point compactification=Aleksandrov one-point compactification
Alexandrov one-point compactification=Alexandrov compactification
Alexandrov one-point compactification=Aleksandrov compactification
Alexandrov one-point compactification=Alexandroff compactification |
Revision comment (for changes between this and next version):
Preamble:
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Content:
The {\em Alexandrov one-point compactification} of a non-compact topological space $X$ is obtained by adjoining a new point $\infty$ and defining the topology on $X\cup\{\infty\}$ to consist of the open sets of $X$ together with the sets of the form $U\cup\{\infty\}$, where $U$ is an open subset of $X$ with compact complement.
With this topology, $X\cup\{\infty\}$ is Hausdorff if and only if $X$ is Hausdorff and locally compact. |
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