Topic summary
Topologist
Extracted from the Wikipedia article Topology.
Motivation
Intuitively, two spaces are homeomorphic if one can be deformed into the other without cutting or gluing. A famous example, known as the "Topologist's Breakfast", is that a topologist cannot distinguish a coffee mug from a doughnut. A pliable torus (shaped like a doughnut) can be reshaped to a coffee mug by creating a dimple and progressively enlarging it while shrinking the central hole into the mug's handle.