Why is the study of mapmaking called topology?

Answer 1

It isn't. You are thinking of topography, the study of surface geographical features. The study of map making as such is cartography.

The etymology of the word topology is from the Greek words, tópos, meaning place, and lógos, meaning reason and discourse. Hence tópos-lógos --> topology --> place-reasoning. From tópos we also get the word topical and from lógos, logic.

Answer 2

Topology is the mathematical study of shapes and spaces that is focused on properties that are preserved through continuous deformations, such as stretching, bending, and twisting. In the context of mapmaking, topology is used to understand spatial relationships and connections without being concerned with exact distances or angles. It helps to identify essential features like connectivity, boundaries, and the number of holes in a space.