Can't get theorems in an appendix

Question

I get the error

\begin{document} ended by \end{theorem}. \end{theorem} and Environment theorem undefined. \begin{theorem}

when trying to compile this latex document.

Here is the problematic code:

\documentclass[a4paper, 12pt, notitlepage]{report}

\usepackage{amsfonts} % if you want blackboard bold symbols e.g. for real numbers
\usepackage{graphicx} % if you want to include jpeg or pdf pictures
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{float}

\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{Def}[thm]{Definition}
\newtheorem{cond}[thm]{Condition}
\newtheorem{rem}[thm]{Remark}
\newtheorem{conj}[]{Conjecture}
\newtheorem*{post}{Postulate 1}
\newtheorem*{post2}{Postulate 2}
\newtheorem*{ex}{Exercise}
\newtheorem{exa}[thm]{Example}

\title{An Introduction to Geometric Measure Theory} % change this
\author{x} % change this
\date{\today} % change this

\numberwithin{equation}{subsection}

\begin{document}    

\appendix
\chapter{Covering Theorems}    

\begin{theorem}
    Let $X$ be boundedly compact metric space and $\mathcal{B}$ a family of closed      balls in $X$ such that 
    \begin{equation}
    sup\{d(B):B \in \mathcal{B}\}
    \end{equation}
\end{theorem}

\end{document}

Answer 1

When you type

\newtheorem{thm}{Theorem}[section]

it means that it will number by sections, write "Theorem" and you refer to it using the environment name thm.

You need to write

\begin{thm}
    Let $X$ be boundedly compact metric space and $\mathcal{B}$ a family of closed      balls in $X$ such that 
    \begin{equation}
    sup\{d(B):B \in \mathcal{B}\}
    \end{equation}
\end{thm}

or you can obtain same result

{\thm
    Let $X$ be boundedly compact metric space and $\mathcal{B}$ a family of closed      balls in $X$ such that 
    \begin{equation}
    sup\{d(B):B \in \mathcal{B}\}
    \end{equation}
}