Symbols:Fonts/mathcal

Font Description

Mathcal is a calligraphic font built into $\LaTeX$.

Its alphabet is displayed here:

Uppercase

$\mathcal {A \ B \ C \ D \ E \ F \ G \ H \ I \ J \ K \ L \ M \ N \ O \ P \ Q \ R \ S \ T \ U \ V \ W \ X \ Y \ Z}$

Lowercase

$\mathcal {a \ b \ c \ d \ e \ f \ g \ h \ i \ j \ k \ l \ m \ n \ o \ p \ q \ r \ s \ t \ u \ v \ w \ x \ y \ z}$

Hence the lowercase letters are not implemented in mathcal, the presentation defaulting to mathit.

Digits

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:

Let $S$ be a set, and let $\powerset S$ be its power set.

$\RR$

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.