We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for...

We comment van Douwen's problems on the Bohr topology of the abelian groups raised in his paper [31] as well as the steps in the solution of some of them. New solutions to two of the resolved problems are also given

An action on a -space induces uniformities on the phase space. It is shown when the maximal -compactification of a -space can be obtained as a completion of the phase space with respect to one of these uniformities. Structure of -spaces with special actions is investigated

The present paper improves a result of [3] by showing that a space is topologically well-orderable if and only if there exists a selection for () which is continuous with respect to the Fell topology on (). In particular, this implies that () has a Fell-continuous selection if and only if () has...

Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem for spaces was already solved by G. E. Strecker in 1966. For certain topologies on...

Given a Dedekind incomplete ordered field, a pair of convergent nets of gaps which are respectively increasing or decreasing to the same point is used to obtain a further equivalent criterion for Dedekind completeness of ordered fields: Every continuous one-to-one function defined on a closed...

In this paper we examine the topology of inverse limit spaces generated by maps of finite graphs. In particular we explore the way in which the structure of the orbits of the turning points affects the inverse limit. We show that if has finitely many turning points each on a finite orbit then...