Theorems, Propositions, Lemmas, …

Suppose you document contains four kinds of theorem-like structures: ``theorems'', ``propositions'', ``conjectures'', and ``wild guesses''. Then near the beginning of the document you should have something like the following:

0.1

 
\newtheorem{thm}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorm{conjec}{Conjecture}
\newtheorem{wildshot}{Hypothesis} % make it sound good!

The first argument to \newtheorem defines a new theorem-like environment name of your own choosing. The second argument contains the text that you want inserted when your theorem is proclaimed:

0.1

\begin{thm} $X$ is normal if, and only if, each pair of disjoint
closed sets in $X$ is completely separated.
\end{thm}

\begin{wildshot} % remember, we chose the name 'wildshot'
The property of Moore extends to all objects of the class $\Sigma$.
\end{wildshot}
which will produce the following:

Theorem 1   X is normal if, and only if, each pair of disjoint closed sets in X is completely separated.

Hypothesis 1   The property of Moore extends to all objects of the class Σ.

Notice that LATEX italicises the theorem statement, and that you still have to shift in to maths mode when you want to set symbols and expression. Typically, it is the style file that determines what a theorem will appear like—so don't go changing this if you are preparing for submission for publication (because the journal staff want to substitute their production style for your document style choice, and not be over-ridden by other commands).