Closed Sets

Some articles on closed sets, closed, set, sets, closed set:

Locally Finite Collection - Closed Sets
... from the definition of a topology that a finite union of closed sets is closed ... One can readily give an example of an infinite union of closed sets that is not closed ... if we consider a locally finite collection of closed sets, the union is closed ...
Characterizations Of The Category Of Topological Spaces - Definition Via Closed Sets
... Objects all pairs (X,T) of set X together with a collection T of subsets of X satisfying The empty set and X are in T ... The intersection of any collection of sets in T is also in T ... The union of any pair of sets in T is also in T ...
More About Closed Sets
... In point set topology, a set A is closed if it contains all its boundary points ... The notion of closed set is defined above in terms of open sets, a concept that makes sense for topological spaces, as well as for other spaces that carry topological structures ... An alternative characterization of closed sets is available via sequences and nets ...
Borel Set
... In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and ... Borel sets are named after Émile Borel ... space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra ...

Famous quotes containing the words sets and/or closed:

    “Yes” shuts us in. “No” sets us free.
    Mason Cooley (b. 1927)

    Pray but one prayer for me ‘twixt thy closed lips,
    Think but one thought of me up in the stars.
    William Morris (1834–1896)