Difference between revisions of "Topological space"
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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 | + | 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 axioms: |
# The empty set and X are elements of T. | # The empty set and X are elements of T. | ||
# The union of any collection of elements in T is in 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. | # The intersection of any finite collection of elements in T is in T. | ||
Elements in T are called [[Open Sets]]. | Elements in T are called [[Open Sets]]. | ||
Revision as of 22:15, 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 axioms:
- 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.