The branch of mathematics concerned with the properties of geometric figures that are preserved under certain deformations (except for tearing), such as stretching, crumpling, etc.
Educational note
Topology differs from geometry in that it essentially focuses on neighbourhoods (closed or open), regions, situations (interior, exterior, boundary) and continuous transformations (deformations), and does not deal with metric aspects (distances, proportions, isometry, similarity), linearity or parallelism, which belong to the domain of geometry.