generated from smyalygames/quartz
554 B
554 B
Definition
Given F \subset \wp(X). The weakest topology on X that contains F is the intersection of all the Topology that contains F. This is a Topology, and consists of \emptyset, X, and all unions of finite intersections of members from F.
[!example]
F \subset \tau\textvisiblespace \cap \tau \ni U_{i} \implies U_{i} \in \tau\implies \cap_{i \in F} \; U_{i} \in \tau \implies \cap U_{i} \in \cap_{F \in \tau} \;\tau
x_{i} \to x\exists jsuch thatx_{i} = x, \; i \geq j.