ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Topology
Bottom topology
Definition D442
Empty topology
Formulation 0
Let $\emptyset$ be the D13: Empty set.
A D11: Set $\mathcal{T} \subseteq \mathcal{P}(\emptyset)$ is an empty topology on $\emptyset$ if and only if \begin{equation} \mathcal{T} = \{ \emptyset \} \end{equation}