From: Bas Spitters <b.a.w.s...@gmail.com>
To: Andrej Bauer <andrej...@andrej.com>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Non-enumerability of R
Date: Sun, 16 Jul 2017 20:35:49 +0200 [thread overview]
Message-ID: <CAOoPQuQMiWYxj8d=4hxJpFxF5QVk7hJQLi8yo5BAVUYqsLdkhw@mail.gmail.com> (raw)
In-Reply-To: <CAB0nkh3PNghRL2+cNWnUU=Zy60c6R1Ypw6b6Zndwewc6T71c_g@mail.gmail.com>
I once gave a proof (without Stone-Weierstrass) in the appendix of this paper:
http://www.cs.au.dk/~spitters/obs.pdf
On Sun, Jul 16, 2017 at 10:11 AM, Andrej Bauer <andrej...@andrej.com> wrote:
>> One then appeals to density of this set by the Stone-Weierstraß theorem: for every continuous function on every open
>> set there is some polynomial in P which intersects its graph, hence R \ P is empty.
>
> In fact, no appeal to Stone-Weierstraß is needed, because that one is
> about *uniform* approximation of functions, whereas we only need local
> approximation. Yes?
>
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next prev parent reply other threads:[~2017-07-16 18:36 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-07-12 9:04 Andrej Bauer
2017-07-12 21:16 ` Andrew Swan
2017-07-16 8:09 ` [HoTT] " Andrej Bauer
2017-07-16 8:11 ` Andrej Bauer
2017-07-16 18:35 ` Bas Spitters [this message]
2017-07-17 13:52 ` Andrej Bauer
2017-07-18 7:54 ` Thomas Streicher
2017-07-18 14:41 ` Nicolai Kraus
2017-07-18 15:28 ` Gaetan Gilbert
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