fiber bundle

A Möbius strip is a fiber bundle which looks locally (i.e., over a connected proper subset of its base space) like the corresponding part of a cylinder S¹⨯[0,1] (a Möbius strip and a cylinder have isomorphic base spaces). A Klein bottle is a fiber bundle which looks locally like the corresponding part of a torus S¹⨯S¹ (again they could be thought of as sharing the same base space S¹; cutting out even a single point of that base space makes the cut Klein bottle isomorphic to the cut torus).