Define a topology on (by listing the open sets within it) that contains the open set (0,2) and (1, 3) and that contains as few open sets as possible.

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- Jan 11th 2009, 03:33 PMr2dee6Topology and Open Set Question
Define a topology on (by listing the open sets within it) that contains the open set (0,2) and (1, 3) and that contains as few open sets as possible.

- Jan 11th 2009, 04:11 PMchabmgph
- Jan 12th 2009, 06:51 AMHallsofIvy
I

**think**the smallest such topology contains 8 sets- but there are several correct answers. - Jan 12th 2009, 08:59 AMchabmgph
- Jan 12th 2009, 09:08 AMlukaszh
It's also important to know: If each set is open, then

are open, if closed then closed. There's also a simple proof. - Jan 12th 2009, 11:00 AMHallsofIvy