Symbols:\mathcal

From ProofWiki
Jump to navigation Jump to search

Font Description

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

Its uppercase alphabet is:

$\AA$ $\BB$ $\CC$ $\DD$ $\EE$ $\FF$ $\GG$ $\HH$ $\II$ $\JJ$ $\KK$ $\LL$ $\MM$ $\NN$ $\OO$ $\PP$ $\QQ$ $\RR$ $\SS$ $\TT$ $\UU$ $\VV$ $\WW$ $\XX$ $\YY$ $\ZZ$


It can also be used to present numbers in a lowercase style thus:

$\mathcal 1$ $\mathcal 2$ $\mathcal 3$ $\mathcal 4$ $\mathcal 5$ $\mathcal 6$ $\mathcal 7$ $\mathcal 8$ $\mathcal 9$ $\mathcal 0$


The lowercase letters are not implemented in Mathcal.


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 $\tuple {X, \tau}$ be a topological space."
"Let $\mathcal B$ 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-O 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.