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

Locally Finite Collection -

... from the definition of a topology that a finite union of

**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

... Objects all pairs (X,T) of

**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

... In point

**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

... 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)

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