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
▼ Bottom topological space
Definition D1112
Empty topological space
Formulation 0
Let $\emptyset$ be the D13: Empty set.
A D548: Ordered pair $T = (X, \mathcal{T})$ is an empty topological space if and only if
(1) $X = \emptyset$
(2) $\mathcal{T} = \{ \emptyset \}$