We study in a constructive manner some problems of topology related to the set Irr of irrational reals. The constructive approach requires a strong notion of an irrational number ; constructively, a real number is irrational if it is clearly different from any rational number. We show that the set Irr is one-to-one with the set Dfc of infinite developments in continued fraction (dfc). We define...

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each r...

It is good to be able to pass on the best wishes of the International Institute of Refrigeration (IIR) and to remind you that the IIR will be holding its Gustav Lorentzen Memorial Conference in Glasgow next year. I hope that the IIR conference will be as well supported and as valuable as this CIBSE/ASHRAE conference. You are warmly invited to attend the Gustav Lorentzen conference in Glasgow, w...

some arguments against infinite regress in islamic philosophy such as applied proof or argument of ones and thousands are based on the mathematical foundations and preliminaries. extraction and analysis of these preliminaries exposes mathematical nature of these arguments and shows that besides philosophical approach to these arguments should also look at them from perspective of mathematics. a...

To any left system of diagram categories or to any left pointed dérivateur a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common properties with Waldhausen’s K-theory. A weaker version of additivity is shown. Also, Quillen’s K-theory of a large class of exact categories including the abelian categories is proved to be a...