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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'' that satisfy the following 3 [[axiom]]s:
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 3 [[axiom]]s:
# The [[empty set]] and ''X'' are elements of ''T''.
# The [[empty set]] and ''X'' are elements of ''T''.
# The [[union_(mathematics)|union]] of any collection of elements in ''T'' is in ''T''.
# The [[union (mathematics)|union]] of any collection of elements in ''T'' is in ''T''.
# The [[intersection]] of any finite 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 set]]s".
Elements in ''T'' are called "[[open set]]s".
[[category: Topology]]
[[Category:Topology]]