K-theory noun3 •The study of rings R generated by the set of vector bundles over some topological space or scheme;K-theory as an independent discipline is a fairly new subject, only about 35 years old. — 1994 •The cohomology generated by the set of vector bundles over some topological space or scheme. •(no longer used, old-fashioned) that part of algebraic topology comprising what is now called topological K-theory.