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 Post subject: set inclusionPosted: Thu, 13 Oct 2011 16:55:16 UTC
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Joined: Thu, 22 Jun 2006 01:08:00 UTC
Posts: 125
hi, can you give me an idea of this?

let and be two metric spaces, let continuous, for

give an example where the inclusion is strict.

I´m not looking for someone to give me the answer, just an idea, thanks

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 Post subject: Re: set inclusionPosted: Thu, 13 Oct 2011 17:10:02 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
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ender wrote:
hi, can you give me an idea of this?

let and be two metric spaces, let continuous, for

give an example where the inclusion is strict.

I´m not looking for someone to give me the answer, just an idea, thanks

You can find them inside .

_________________

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 Post subject: Re: set inclusionPosted: Thu, 13 Oct 2011 17:58:56 UTC
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Joined: Thu, 7 Apr 2005 16:32:15 UTC
Posts: 1276
Location: United States EST
Let f:R->R be a function where R is the reals.

Okay, the closure of f(A) is basically points approached by y-values of the graph.
Let . Suppose , then f(x)=y for some x in .

So if you don't want y in , you can't have f(x)=y for any x in A and you can't have f(x)=y for any x real with for some sequence .

Thus, a continuous function with a horizontal asymptote it never crosses should be fine, there are tons of functions like this.

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