From: Victor Porton <por...@narod.ru>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Another variation on the topic of homotopy
Date: Thu, 1 Mar 2018 08:22:33 -0800 (PST) [thread overview]
Message-ID: <1f0cc7d4-23d4-4458-bf0b-428a5cc8dd39@googlegroups.com> (raw)
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I have the following (very preliminary) idea:
Replace “path” in the definition of homotopy with “monovalued funcoid with
domain [0;1]”. It enables things like infinitely short paths. (Consider
such things as a plane without a point and an infinitely short path around
this point, yet to be formulated precisely.) This "generalized path" is a
mapping from [0;1] to ultrafilters (with certain restriction these
ultrafilters conform to).
This way we may get another HoTT possibly not equivalent to the “main”
HoTT. Moreover, we may probably construct several non-equivalent theories
(needs careful consideration).
I have not yet formulated this precisely, but call you as soon as the rough
idea appeared, so that you become able for example learn my theory of
funcoids and start to ponder about my idea. I am going to write again when
this will be formulated exactly. But you are free to join my research and
race with me who will first have enough time to formulate this in details.
This idea uses theory of funcoids
<http://www.mathematics21.org/algebraic-general-topology.html> (discovered
by me). By the way, please consider to nominate me for Breakthrough Prize
for discovery (and thorough research) of the concept of funcoid. I need
money. (Not three millions, I would probably donate two of them to some
charity.)
Disclaimer: I am in no way an expert in homotopy and HoTT. But this my idea
is probably great.
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