From f04baf15703609c99b7eb20d77a68cf038469f7b Mon Sep 17 00:00:00 2001 From: Nikolai Kudasov Date: Mon, 31 Jul 2023 11:05:31 +0300 Subject: [PATCH] Fix some typos and add a reference in circle.tex --- circle.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/circle.tex b/circle.tex index 3668bc82..fb65a9c0 100644 --- a/circle.tex +++ b/circle.tex @@ -551,7 +551,7 @@ \section{\Coverings} two points (i.e., each preimage can be merely identified with $\bool$). However, $A$ is not the constant family, like $A'$ depicted on the right, since we have a string of equivalences -$A'\defeq\sum_{z:\Sc}\bool\eqto(\Sc\times\bool)\eqto(\Sc+\Sc)$, +$A'\defeq\sum_{z:\Sc}\bool\eqto(\Sc\times\bool)\eqto(\Sc\amalg\Sc)$, and the latter type is not connected. Obviously something way more fascinating is going on. @@ -578,7 +578,7 @@ \section{\Coverings} \node[fill,circle,inner sep=1pt] at (-1,1) {}; % \node (L) at (1,-3) {(left)}; \begin{scope}[xshift=6cm] - \node (At) at (2,1) {$\Sc+\Sc$}; + \node (At) at (2,1) {$\Sc\amalg\Sc$}; \node (Bt) at (2,-2) {$\Sc$}; \draw[->] (At) -- (Bt); \draw (0,-2) ellipse (1 and .3); @@ -1162,7 +1162,7 @@ \section{The symmetries in the circle} We note in passing that combining the above two exercises yields an equivalence from $(\Sc\eqto\Sc)$ to $(\Sc\amalg\Sc)$, -that is, a characterization of the symmetries \emph{of} the cycle +that is, a characterization of the symmetries \emph{of} the circle (in constrast to the title of this \cref{sec:symcirc}). @@ -2144,7 +2144,7 @@ \section{Connected \coverings over the circle} The Limited Principle of Omniscience (\cref{LPO}) implies that the type of connected decidable \coverings over the circle is the sum of the component containing the universal \covering and for each positive integer $m$, -the component containing the $m$-fold \covering. +the component containing the $m$-fold \covering (\cref{def:mfoldS1cover}). \end{lemma} \begin{remark}