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In this paper, we study some semi-closed 1-set-contractive operators A and investigate the boundary conditions under which the topological degrees of 1-set contractive fields, deg , , I A p are equal to 1. Correspondingly, we can obtain some new fixed point theorems for 1-set-contractive operators which extend and improve many famous theorems such as the Leray-Schauder theorem, and operator equation, etc. Lemma 2.1 generalizes the famous theorem. The calculation of topological degreesdoi:10.4236/am.2012.38127 fatcat:n6ng4aem75ecfokl2i4dtrxhfm