A Royal Road to Topology

Convergence theory is intuitive, that it is highly operational, results from its universality (which will become evident from the lecture of this book). In plain words, the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Convergence theory exponentially completes topology in an analogous way as the field of complex numbers algebraically completes the field of real numbers. The title of this book alludes 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 most cases, they appear as simple consequences of the developed theory of convergence.