In this paper, a collection of sets are investigated in such way that the splits preopen and b-open also semi-open sets. Functions terms is part paper it will be considered these remains invariant under homeomorphic image.

A δ-uniform BSS machine is a standard BSS machine which does not rely on exact equality tests. We prove that, for any real closed archimedean field R, a set is δ-uniformly semi-decidable iff it is open and semi-decidable by a BSS machine which is locally time bounded; we also prove that the local time bound condition is nontrivial. This entails a number of results about BSS machines, in particu...

We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semialgebraic sets. Aside from describing these results, we discuss briefly the background as well as the importance of these problems, and also describe the main tools from algorithmic semi-al...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

This paper is a survey on SPG-reguli, SPG-systems, BLT-sets and sets with the BLT-property. It is shown how from these sets generalized quadrangles, partial geometries and semi-partial geometries can be constructed. Many examples are given and open problems are stated. There are also some new results. c © 2007 Elsevier B.V. All rights reserved.