sums of compact pavings are compact
Suppose that is a paved space for each in an index set . The direct sum, or disjoint union (http://planetmath.org/DisjointUnion), is the union of the disjoint sets . The direct sum of the paving is defined as
Let be compact paved spaces for . Then, is a compact paving on .
The paving consisting of subsets of of the form where for all but a single is easily shown to be compact. Indeed, if satisfies the finite intersection property then there is an such that for every . Compactness of gives .
|Title||sums of compact pavings are compact|
|Date of creation||2013-03-22 18:45:15|
|Last modified on||2013-03-22 18:45:15|
|Last modified by||gel (22282)|
|Synonym||disjoint unions of compact pavings are compact|
|Defines||direct sum of pavings|
|Defines||disjoint union of pavings|