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star refinement
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(Definition)
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Let be a set and
be a cover of (we assume and are all subsets of some universe). Let
. The star of (with respect to the cover
) is defined as
When is a singleton, we write
.
Properties of 
-
.
- If
, then
.
- For any cover
of , the sets
and
are both covers of .
-
( denotes cover refinement).
Definitions. Let
be two covers of . If
, then we say that
is a star refinement of
, denoted by
. If
, then we say that
is a barycentric refinement of
, denoted by
.
Remark. By property 4 above, it is easy to see that
.
- 1
- S. Willard, General Topology, Addison-Wesley, Publishing Company, 1970.
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"star refinement" is owned by CWoo.
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(view preamble)
| Also defines: |
star, star refine, barycentric refinement |
This object's parent.
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Cross-references: easy to see, definitions, refinement, properties, singleton, universe, subsets, cover
There are 13 references to this entry.
This is version 3 of star refinement, born on 2007-02-23, modified 2007-05-26.
Object id is 8959, canonical name is StarRefinement.
Accessed 1244 times total.
Classification:
| AMS MSC: | 54A99 (General topology :: Generalities :: Miscellaneous) |
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Pending Errata and Addenda
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