This book explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods.
Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry.
This book explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods.
This book offers several topics of mathematical analysis which are closely connected with significant properties of real-valued functions of various types (such as... Læs mere