Some fundamental ideas in topology and their application to problems in metallurgy

Abstract

The topological ideas and results that have been used by metallurgists, together with several results not previously presented in the metallurgical literature, are developed in a systematic manner. Based on this presentation, a review is given of the use of topology in metallurgy. The additional topology that is introduced includes the Alexander duality theorem, the Euler-Poincare formula, and the concept of deformation retract. These concepts are used to establish interrelationships among the results of several papers and to clarify the mathematical treatment.