Topological geometry deals with incidence structures consisting of a point set P {\displaystyle P} and a family L {\displaystyle {\mathfrak {L}}} of subsets of P {\displaystyle P} called lines or circles etc. such that both P {\displaystyle P} and L {\displaystyle {\mathfrak {L}}} carry a topology and all geometric operations like joining points by a line or intersecting lines are continuous.
Topological geometry deals with incidence structures consisting of a point set P {\displaystyle P} and a family L {\displaystyle {\mathfrak {L}}} of subsets of P {\displaystyle P} called lines or circles etc. such that both P {\displaystyle P} and L {\displaystyle {\mathfrak {L}}} carry a topology and all geometric operations like joining points by a line or intersecting lines are continuous.
Source: Wikipedia "Topological geometry" · CC BY-SA 4.0
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