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 3 axioms: | + | 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 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]]. |
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 05:28, April 12, 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 3 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.