Shape theory (mathematics)

From Wikipedia, the free encyclopedia

Shape theory is part of the mathematical field of topology. Its overall goal is to extend results from homotopy theory for spaces with good local properties, like CW complexes, to compact metric spaces or compact Hausdorff spaces.

Shape theory was founded by the Polish mathematician Karol Borsuk in 1968. Borsuk lived and worked in Warsaw, hence the name of one of the fundamental examples of the area, the Warsaw circle. This is a compact subset of the plane produced by "closing up" a topologist's sine curve with an arc. It has homotopy groups isomorphic to those of a point, but is not homotopy equivalent to it; Whitehead's theorem does not apply because the Warsaw circle is not a CW complex.

[edit] References

• Mardešić, Sibe (1997). "Thirty years of shape theory" (PDF). Mathematical Communications 2: 1–12. http://hrcak.srce.hr/file/2848.