Topology is the mathematical study of the most basic geometrical
structure of a space. Mathematical physics uses topological spaces
as the formal means for describing physical space and time. This
book proposes a completely new mathematical structure for
describing geometrical notions such as continuity, connectedness,
boundaries of sets, and so on, in order to provide a better
mathematical tool for understanding space-time. This is the initial
volume in a two-volume set, the first of which develops the
mathematical structure and the second of which applies it to
classical and Relativistic physics. The book begins with a brief
historical review of the development of mathematics as it relates
to geometry, and an overview of standard topology. The new theory,
the Theory of Linear Structures, is presented and compared to
standard topology. The Theory of Linear Structures replaces the
foundational notion of standard topology, the open set, with the
notion of a continuous line. Axioms for the Theory of Linear
Structures are laid down, and definitions of other geometrical
notions developed in those terms. Various novel geometrical
properties, such as a space being intrinsically directed, are
defined using these resources. Applications of the theory to
discrete spaces (where the standard theory of open sets gets little
purchase) are particularly noted. The mathematics is developed up
through homotopy theory and compactness, along with ways to
represent both affine (straight line) and metrical structure.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
