Re: defining a closed set
- From: MoeBlee <jazzmobe@xxxxxxxxxxx>
- Date: Tue, 28 Oct 2008 11:20:55 -0700 (PDT)
On Oct 27, 8:48 pm, RichD <r_delaney2...@xxxxxxxxx> wrote:
d(x) = distance from origin
A = {x | d(x) < 1}
A is an open set.
B = {x | d(x) = 1}
B is the boundary of A.
C = A U B
C is a closed set. QED
QED? What is the what proposition do you think you've proven?
Look at my post. I anticipated what you're driving at:
closure(S) = interior(S) u boundary(S).
And, of course, we know that the closure of any set is a closed set.
But that doesn't entail that
C is closed iff there is an open set S such that C = S u boundary(S).
You seem to be confusing two related, but different things:
(1) The defintion of a 'closed set'.
and
(2) The fact that the closure of any set is the union of the interior
and boundary of that set and that the closure of any set is a closed
set.
MoeBlee
.
- References:
- defining a closed set
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- Re: defining a closed set
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- Re: defining a closed set
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