**discrete topological space**if and only if

(1) | $X$ is a D11: Set |

(2) | $\mathcal{T} = \mathcal{P}(X)$ (D134: Discrete topology) |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Topological space

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Topological space

Formulation 0

An D548: Ordered pair $T = (X, \mathcal{T})$ is a **discrete topological space** if and only if

(1) | $X$ is a D11: Set |

(2) | $\mathcal{T} = \mathcal{P}(X)$ (D134: Discrete topology) |