Abstract: We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.
Abstract: In this paper we will constructively prove the existence
of an equilibrium in a competitive economy with sequentially locally
non-constant excess demand functions. And we will show that the
existence of such an equilibrium in a competitive economy implies
Sperner-s lemma. We follow the Bishop style constructive mathematics.
Abstract: We examine the maximum theorem by Berge from the
point of view of Bishop style constructive mathematics. We will show
an approximate version of the maximum theorem and the maximum
theorem for functions with sequentially locally at most one maximum.