Discussion of Homotopy Type Theory and Univalent Foundations
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From: Andrej Bauer <andrej...@andrej.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Non-enumerability of R
Date: Sun, 16 Jul 2017 09:11:18 +0100	[thread overview]
Message-ID: <CAB0nkh3PNghRL2+cNWnUU=Zy60c6R1Ypw6b6Zndwewc6T71c_g@mail.gmail.com> (raw)
In-Reply-To: <CAB0nkh3cXQN46Nx6s_FsYiNQJ=bUOYS7QfcBThUFdkpb0=vbGQ@mail.gmail.com>

> 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?

  reply	other threads:[~2017-07-16  8:11 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 [this message]
2017-07-16 18:35       ` Bas Spitters
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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