Empty Set is Open

Theorem

Topological Space

Let $T = \struct {X, \tau}$ be a topological space.

Then the empty set $\O$ is an open set of $T$.

Metric Space

Let $M = \struct {A, d}$ be a metric space.

Then the empty set $\O$ is an open set of $M$.

Normed Vector Space

Let $M = \struct {X, \norm {\, \cdot \,}}$ be a normed vector space.

Then the empty set $\O$ is an open set of $M$.

Neighborhood Space

Let $\struct {S, \NN}$ be a neighborhood space.

Then the empty set $\O$ is an open set of $\struct {S, \NN}$.