Not only is it a closed surface, you can get it by doing the same kind of thing you'd do with a square to turn it into a torus. You join the top and bottom edges like you would in a torus, but you join the left and right edges with a half-twist, so the bottom of one is joined to the top of the other and vice versa.
Don't try to do it, you can't in three dimensions :) But the resulting identification space is definitely a Klein bottle.
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timeasmymeasure
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Date: 2005-11-14 05:34 pm (UTC)Don't try to do it, you can't in three dimensions :) But the resulting identification space is definitely a Klein bottle.