About this deck
homeomorphism Same shape, different presentation. The puzzle To a topologist, a coffee cup is a donut. Stretch, bend, twist — but never cut, never glue. Under such deformations the cup with one handle and the torus with one hole are indistinguishable. Both are surfaces of genus one. Key sections include: TOPOLOGY / Shape without measurement; To a topologist, a coffee cup is a donut.; Euler and the seven bridges of Königsberg.; Topology studies properties preserved under continuous deformation.; A topological space is a set with a chosen family of open sets.; Euler characteristic.; The Möbius strip : one side, one edge.; The Klein bottle : a surface with no inside.; Closed loops in space, classified up to ambient isotopy.; Translate shapes into groups..