In mathematical mode as well as in text mode, you can change the typeface as needed. For instance, it's customary to represent real numbers with a blackboard bold font, or topological spaces with calligraphic font. This article shows several fonts for use in math mode.
For some elements is convenient to have the possibility of changing the font typeface.
Let \( \mathcal{T} \) be a topological space, a basis is defined as
\[
\mathcal{B} = \{B_{\alpha} \in \mathcal{T}\, |\, U = \bigcup B_{\alpha} \forall U \in \mathcal{T} \}
\]
Several fonts require the addition of the line \usepackage{amssymb}
to the preamble to work.
There are some font typefaces that support only a limited number of characters; these fonts usually denote some special sets.
\begin{align*}
RQSZ \\
\mathcal{RQSZ} \\
\mathfrak{RQSZ} \\
\mathbb{RQSZ}
\end{align*}
This example shows Calligraphic, Fraktur and Blackboard bold typefaces. For instance, to display the R in blackboard bold typeface $\mathbb{R}$
will do the trick.
It's possible to set a different font family for a complete mathematical expression.
\begin{align*}
3x^2 \in R \subset Q \\
\mathnormal{3x^2 \in R \subset Q} \\
\mathrm{3x^2 \in R \subset Q} \\
\mathit{3x^2 \in R \subset Q} \\
\mathbf{3x^2 \in R \subset Q} \\
\mathsf{3x^2 \in R \subset Q} \\
\mathtt{3x^2 \in R \subset Q}
\end{align*}
In this case, not only letters but all characters change its appearance, for example $\mathit{3x^2}$
italicises the entire expression.
For more information see