The two definitions seem very similar to me and is confusing.

To express it simply

a basis generates a topology T and a subbasis generates a basis for a topology?

Is there an example that could clarify this difference?

Thank you for your help.

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- Dec 6th 2011, 09:58 PMJameThe difference between and basis and subbasis for a topology
The two definitions seem very similar to me and is confusing.

To express it simply

a basis generates a topology T and a subbasis generates a basis for a topology?

Is there an example that could clarify this difference?

Thank you for your help. - Dec 6th 2011, 10:06 PMDrexel28Re: The difference between and basis and subbasis for a topology

Roughly, bases are collections of subsets by which all open sets can be obatined via unions from that family and subbases are collection of open subsets for which any open subset can be obtained by unions of INTERSECTIONS of elements of the collection. For example the set of all infinite rectangles $\displaystyle \{\mathbb{R}\times (a,b):a,b\in\mathbb{R}\}$ forms a subbasis for the usual topology on $\displaystyle \mathbb{R}^2$ but not a basis. Explain to me why. - Dec 7th 2011, 08:58 AMJameRe: The difference between and basis and subbasis for a topology
Oh i see. There are open sets in $\displaystyle \mathBB{R}^2$ which we cannot get from unioning these infinite rectangles together, but they can be made by unioning intersects of these rectangles.

Thank you for thee clarification. That is a really good example.