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A set of subsets of a set (or space) containing the empty subset. The elements of the paving are called stones. A set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718701.png" /> together with a paving <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718702.png" /> forms a paved space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718703.png" />. A compact paving (a compact paved space) is a paving <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718704.png" /> (a paved space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718705.png" />) with the finite intersection property: for every finite subset <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718706.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071870/p0718707.png" /> is non-empty.
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A set of subsets of a set (or space) containing the empty subset. The elements of the paving are called stones. A set $  \Omega $
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together with a paving $  {\mathcal C} $
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forms a paved space $  ( \Omega , {\mathcal C} ) $.  
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A compact paving (a compact paved space) is a paving $  {\mathcal C} $(
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a paved space $  ( \Omega , {\mathcal C} ) $)  
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with the finite intersection property: for every finite subset $  \{ C _ {1} \dots C _ {n} \} \subset  {\mathcal C} $,  
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$  \cap _ {i=} 1  ^ {n} C _ {i} $
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is non-empty.
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M.M. Rao,  "Measure theory and integration" , Wiley (Interscience)  (1987)  pp. Chapt. 7</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M.M. Rao,  "Measure theory and integration" , Wiley (Interscience)  (1987)  pp. Chapt. 7</TD></TR></table>

Latest revision as of 08:05, 6 June 2020


A set of subsets of a set (or space) containing the empty subset. The elements of the paving are called stones. A set $ \Omega $ together with a paving $ {\mathcal C} $ forms a paved space $ ( \Omega , {\mathcal C} ) $. A compact paving (a compact paved space) is a paving $ {\mathcal C} $( a paved space $ ( \Omega , {\mathcal C} ) $) with the finite intersection property: for every finite subset $ \{ C _ {1} \dots C _ {n} \} \subset {\mathcal C} $, $ \cap _ {i=} 1 ^ {n} C _ {i} $ is non-empty.

References

[a1] M.M. Rao, "Measure theory and integration" , Wiley (Interscience) (1987) pp. Chapt. 7
How to Cite This Entry:
Paving. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Paving&oldid=17232
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