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upper semicontinuous decomposition

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upper semicontinuous decomposition [′əp·ər ¦sem·i·kən′tin·yə·wəs dē‚käm·pə′zish·ən]
(mathematics)
A partition of a topological space with the property that for every memberDof the partition and for every open setUcontainingDthere is an open setVcontainingDwhich is contained inUand is the union of members of the partition.


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Daverman covers the preliminaries in terms of elementary properties of upper semicontinuous decompositions, upper semicontinuous decompositions, proper maps and monotome decompositions, the shrinkabilty criterion, cell-like decompositions of absolute neighborhood retracts, the cell-like approximation theorem, shrinkable decompositions, nonshrinkable decompositions, and applications to manifolds.
 
 
 
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