Being homotopic is an equivalence relation on the set of all continuous functions from X to Y. This homotopy relation is compatible with function …

6 days ago · Another way of saying this is that a homotopy is a path in the mapping space from the first function to the second. Two mathematical objects …

Two paths with common endpoints are called homotopic if one can be continuously deformed into the other leaving the end points fixed and remaining …

The quest to study topological spaces up to homotopy equivalence has a natural starting point — we begin by asking which spaces are the least …

Formation of sets of homotopy classes of maps leads to a new category, the homotopy category (of spaces) HoTop. The objects of HoTop are the same …

Today, I'll give an introduction to a basic notion in homotopy theory, namely the notion of homotopy groups. The hope is that you develop an intuition for …

Topological spaces X; Y are said to be homotopy equivalent(or homotopic or have the same homotopy type X ' Y ) when they are isomorphic in the …

Feb 14, 2026 · Being homotopic is an equivalence relation on the set of all continuous functions from X to Y. This homotopy relation is compatible with …

For each n-connected CW pair (X, A) there is a CW pair (Z, A) that is homotopy equivalent to (X, A) relative to A, and such that Z is built from A by …

A homotopy of paths in X is a family f t: I → X, 0 ≤ t ≤ 1, such that When two paths f 0 and f 1 are connected in this way by a homotopy f t, they are said to …