There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the (...) algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs. (shrink)

Zeno argued that since at any instant an arrow does not change its location, the arrow does not move at any time, and hence motion is impossible. I discuss the following three views that one could take in view of Zeno's argument:(i) the "at-at" theory, according to which there is no such thing as instantaneous velocity, while motion in the sense of the occupation of different locations at different times is possible,(ii) the "impetus" theory, according to which instantaneous velocities do (...) exist but these are only contingently and causally related to the temporal developments of positions,(iii) the "no instants" theory, according to which instants in time do not exist, and hence instantaneous velocities do not exist, while motion, in the sense of different areas occupied during different time intervals, is possible.I argue that, despite the fact that there have been interesting and relevant developments in mathematics and physics since the time of Zeno, each of these views still has serious drawbacks. (shrink)

A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...) functions and those that do correspond to continuous functions. (shrink)

There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.