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Universe (Set Theory)

$\mathbb U$

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 $\LaTeX$ code for \(\mathbb U\) is \mathbb U .

Open Set


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

The $\LaTeX$ code for \(U\) is U .