Librería Samer Atenea
Librería Aciertas (Toledo)
Kálamo Books
Librería Perelló (Valencia)
Librería Elías (Asturias)
Donde los libros
Librería Kolima (Madrid)
Librería Proteo (Málaga)
The aim of this book is threefold: to reinstate distance functions as a principaltool of general topology, to promote the use of distance functions on variousmathematical objects and a thinking in terms of distances also in nontopologicalcontexts, and to make more specific contributions to distancetheory.We start by learning the basic properties of distance, endowing all kinds ofmathematical objects with a distance function, and studying interesting kindsof mappings between such objects. This leads to new characterizations ofmany well-known types of mappings. Then a suitable notion of distancespaces is developed, general enough to induce most topological structures,and we study topological properties of mappings like the concept of stronguniform continuity.Important results include a new characterization of the similarity mapsbetween Euclidean spaces, and generalizations of completion methods andfixed point theorems, most notably of the famous one by Brouwer. We closewith a short study of distance visualization techniques.
