Symbols:Fonts/mathcal
Font Description
Mathcal is a calligraphic font built into $\LaTeX$.
Its alphabet is displayed here:
- $\mathcal {A \ B \ C \ D \ E \ F \ G \ H \ I \ J \ K \ L \ M \ N \ O \ P \ Q \ R \ S \ T \ U \ V \ W \ X \ Y \ Z}$
- $\mathcal {a \ b \ c \ d \ e \ f \ g \ h \ i \ j \ k \ l \ m \ n \ o \ p \ q \ r \ s \ t \ u \ v \ w \ x \ y \ z}$
Hence the lowercase letters are not implemented in mathcal, the presentation defaulting to mathit.
The Mathcal font can be used to present the digits in a lowercase style thus:
- $\mathcal {1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 \ 0}$
The individual letters of this font and their various uses on $\mathsf{Pr} \infty \mathsf{fWiki}$ are listed on this page as well as on the pages for the letters themselves.
For the uppercase alphabet, $\mathsf{Pr} \infty \mathsf{fWiki}$ has defined some custom $\LaTeX$ commands for convenience, in the following way:
- The $\LaTeX$ code for \(\AA\) is
\AA
. - The $\LaTeX$ code for \(\BB\) is
\BB
.
and so on.
For numbers, the conventional coding is used:
- The $\LaTeX$ code for \(\mathcal 1\) is
\mathcal 1
. - The $\LaTeX$ code for \(\mathcal 2\) is
\mathcal 2
.
$\BB$
This is used to denote a basis in topology.
An example of an introduction of this would be:
- "Let $\struct {X, \tau}$ be a topological space."
- "Let $\BB$ be a basis for $\tau$."
$\CC$
This is used to denote a cover.
An example of an introduction of this would be:
- Let $S$ be a set.
- Let $\CC$ be a cover for $S$.
$\OO$
This is used for big-$\OO$ notation.
$\PP$
This is used to denote power set.
To introduce the power set of a set $S$ we would state:
$\RR$
This is used for binary relations.
For example to introduce a binary relation on $S \times T$ we would state:
- Let $\RR \subseteq S \times T$ be a relation.