Definition:Open Set (Topology)

Definition

Let $T = \left({X, \vartheta}\right)$ be a topological space.

Then the elements of $\vartheta$ are called the open sets of $T$.

Thus:

$U \in \vartheta$

and:

$U$ is open in $T$

are equivalent statements.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$