Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, en…
Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysic…
Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum ca…
Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum ca…
Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysic…
The embeddability and structure of all locally compact one-to-one continuous metric (equivalently, Hausdorff) images of the real line are studied. The structure of such spaces is utilized to obtain, for example, necessary and sufficient conditions that they be embeddable in the …
Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This text explores the key idea…
