Topology: from Lefschetz to Euler

According to Webster's, topology is defined as the study of those properties of geometric figures that remain unchanged even when under distortion, so long as no surfaces are torn. The word topology was coined in 1930 by the mathematician Solomon Lefschetz; who was a pioneer in the developing of the algebraic techniques of the topic.
Usually classified under geometry, topology has is often referred to as rubber band, rubber-sheet, or rubber-space geometry, due to the properties of a topological figure. Others call it the study of continuity, being that all topological figures have but o…