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looks like a good start. made what i think is a correction -- see talk page
Open intervals are not the only open sets. Any union of open intervals is an open set. For example:
Open intervals are not the only open sets. Any union of open intervals is an open set. For example:
<!--
::<math>\{ N, N+1/N\ |\ N \textrm{\ is\ an\ integer} \ge 2 \}</math>
::<math>\{ N, N+1/N\ |\ N \textrm{\ is\ an\ integer} \ge 2 \}</math>
-->
::<math>\bigcup_{N \textrm{\ is\ an\ integer\ } \geq 2} (N,N+1/N)</math>
Bizarrely defined sets like the one above are commonly used as examples and counterexamples in analysis and topology.
Bizarrely defined sets like the one above are commonly used as examples and counterexamples in analysis and topology.
[[category:mathematics]]
[[category:mathematics]]