होमोटोपी इसके अंग्रेजी अर्थ का उदाहरण

In finite-dimensional Morse theory, different choices made in constructing the vector field on X "times; I yield distinct but chain homotopic maps and thus descend to the same isomorphism on homology.

We say that x is equivalent to y if and only if there exists a path c from x to y with f(c) homotopic to c as paths.

The homotopy quotient, also called homotopy orbit space or Borel construction, is a “homotopically correct” version of the orbit space (the quotient of X by its G-action) in which X is first replaced by a larger but [equivalent] space so that the action is guaranteed to be free.

The objects are the points in the space X, morphisms are homotopy classes of paths between points, and higher morphisms are higher homotopies of those points.