What familiar space is the quotient -complex of a 2-simplex obtained by identifying the edges and , preserving the ordering of vertices?

This is a question from Hatcher. So if we “glue” two edges of the triangle together, preserving order, we get a Mobius Strip!

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Thanks for this simple, yet inspirational example from Hatcher. It reminds that Prof. Allen Hatcher’s Notes on Topology are available somewhere from web. (I had downloaded them long back). BTW, it inspires me to put some stuff on mobius strip for fun in my own blog ! đź™‚

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Professor Hatcher is very generous to put up his book for free. Certainly one of the best Algebraic Topology resources!

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When you say “glue” two edges together we can make an MĂ¶bius strip, can further explain your discovery with an example?

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Sure. An example would be to take a long rectangular strip of paper, make a twist and glue the ends together. For a detailed guide check out http://m.wikihow.com/Make-a-Mobius-Strip

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Can this be done on a computer or computer program?

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I believe it can be done.

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Do you have any examples using computers?

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http://curvebank.calstatela.edu/moebius/moebius.htm

This is one example.

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