Difference between revisions of "Topological space"
Jump to navigation
Jump to search
(bold, links) |
|||
| Line 1: | Line 1: | ||
| − | A | + | 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 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 [[ | + | Elements in ''T'' are called "[[open set]]s". |
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 00:53, May 28, 2008
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".