Shape theory (mathematics)

Shape theory was invented and published by D. E. Christie in 1944; it was reinvented, further developed and promoted by the Polish mathematician Karol Borsuk in 1968.

So by the Whitehead theorem, the Warsaw circle does not have the homotopy type of a CW complex.

This was done in a continuous style, characteristic for the Čech homology rendered by Samuel Eilenberg and Norman Steenrod in their monograph Foundations of Algebraic Topology.

For some purposes, like dynamical systems, more sophisticated invariants were developed under the name strong shape.

Generalizations to noncommutative geometry, e.g. the shape theory for operator algebras have been found.