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.
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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.
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