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I read a little remark in a topology text that the direct image of an open set under a continuous mapping is not necessarily open.

What is the definition of direct image in this case? I tried googling to no avail, and only found references to sheaf theory on wikipedia, which I don't believe to be what I'm looking for. Thanks.

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1 Answer 1

They just mean "image". An example here is the image of the set $(0, 2\pi)$ under the map $\sin(x)$, which is $(0, 1]$.

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Thanks, I thought it may have meant something else, but I'd never heard such a phrase. –  meezy Nov 8 '10 at 13:02
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It may be that they are trying to make a contrast with "inverse image". I would say "forward image" but this author seems to say "direct image" instead. –  Carl Mummert Nov 8 '10 at 13:03

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