Difference between revisions of "Topological space"

Revision as of 22:14, March 14, 2007

A Topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X that satisfy the following properties:

Elements in T are called Open Sets.

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-A Topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X called [[Open Sets]].
+A Topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X that satisfy the following properties:
+# The empty set and X are elements of T.
+# The union of any collection of elements in T is in T.
+# The intersection of any finite collection of elements in T is in T.
+Elements in T are called [[Open Sets]].