A theoretical constructivisation of mathematical economics

This thesis deals with some problems in mathematical economics, looked at constructively; that is, with intuitionistic logic. In particular, we look at the connection between approximate Pareto optima and approximate equilibria. We then examine the classically vacuous, but constructively nontrivial, problem of locating the exact point where a line segment crosses the boundary of a convex subset of RN. We also prove the pointwise continuity of an associated boundary crossing mapping. Turning to a rather different aspect of the theory, we discuss Ekeland's Theorem giving approximate minima of certain functions, as well as some fundamental notions in related areas of optimisation. The thesis ends with a discussion of some problems associated with the possible constructivisation of McKenzie's proof of the existence of competitive equilibria

Sequentially Continuous Linear Mappings in Constructive Analysis

this paper we derive some results about sequentially continuous linear mappings within BISH. These results tend to reinforce our hope that such mappings may turn out to be bounded (continuous) after all. For background material on BISH, see [1], and for information about the relation between BISH, INT, and RUSS, see [2]. 2 Sequential continuity preserves Cauchynes