Topological Space
Natural & Formal Sciences Dictionary
Definition
A set X together with a collection τ of subsets of X (called open sets) such that ∅ and X belong to τ, τ is closed under arbitrary unions and finite intersections; τ is called a topology and (X, τ) is a topological space.
Topological Space
- Natural & Formal Sciences -
Mathematics & Logic Dictionary
Definition
A set equipped with a topology: a specified collection of open subsets that contains the empty set and the whole set, is closed under arbitrary unions and finite intersections.
Topological Space
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
A set X equipped with a collection τ of subsets called open sets such that the empty set and X belong to τ, arbitrary unions of members of τ belong to τ, and finite intersections of members of τ belong to τ.