Royal Road To Topology, A: Convergence Of Filters

Convergence theory completes topology in an analogous way as the field of complex numbers algebraically completes the field of real numbers. The class of convergences is closed under several natural, essential operations, under which the class of topologies is not!Convergence theory is intuitive and operational. This results from a right level of abstraction of the theory, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal. The title of this book alludes to the mentioned advantages of the present approach, which I believe to be more gratifying than many traditional ones: you travel more comfortably and see more. Principal classical topics of typical topology courses are included. In many cases, they appear as simple consequences of the developed theory of convergence.