# Symbols:U

### Universe

- $\mathbb U$

Sets are considered to be subsets of some large **universal set**, also called the **universe**.

Exactly what this **universe** is will vary depending on the subject and context.

When discussing particular sets, it should be made clear just what that **universe** is.

However, note that from There Exists No Universal Set, this **universe** cannot be *everything that there is*.

The traditional symbol used to signify the **universe** is $\mathfrak A$.

However, this is old-fashioned and inconvenient, so some newer texts have taken to using $\mathbb U$ or just $U$ instead.

With this notation, this definition can be put into symbols as:

- $\forall S: S \subseteq \mathbb U$

The use of $\mathbb U$ or a variant is not universal: some sources use $X$.

The $\LaTeX$ code for \(\mathbb U\) is `\mathbb U`

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### Open Set

- $U$

Frequently used, and conventionally in many texts, to denote an open set in the context of topology.

The $\LaTeX$ code for \(U\) is `U`

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