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Topic: help with misprint (?) Counterexamples in topology
Replies: 9   Last Post: Feb 15, 2013 8:54 AM

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Posts: 1,968
Registered: 12/4/12
Re: Minimal Hausdorff Topology
Posted: Feb 14, 2013 12:41 PM
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In 2/14/2013 9:38 AM, Shmuel (Seymour J.) Metz wrote:
> In <>, on 02/11/2013
> at 09:38 PM, fom <> said:

>> You may be unaware that identity in set theory
>> is not the same as what you have described with
>> your explanation above.

> He wrote "indistiguishable", which is a differnet notion.

The full text of the original post was about identity.

It was about a particular form of stipulative identity
that arises when considering the definition of the
real numbers in terms of Dedekind cuts.

At the end of the post, the mechanism used to do the
analysis was re-interpreted so that its topological
aspects could be considered.

Certainly, you are correct that there are various
contexts. But, one aspect of foundational
investigations is to sort out the logical priority
of structures.

I am fully aware of much that is written in
topology texts. The last part of that post
points out that any countable language with a
sign of negation and interpretation with respect
to bivalent logic may possibly be represented
with a minimal Hausdorff topology.

So, is topology foundational?

Can't seem to get a discussion on *hard* questions.

Thank you for your observation, however. I shall
try to be more careful when explaining myself in
the future.

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