-The book is an elegant piece of work, suitable as a text for the beginning student as well as pleasant and informative reading for the mature mathematician. Both the topologist and the analyst might profit from its inclusion in their libraries.- -- Scripta Mathematica The author's previous book on point-set topology, also translated by Professor Krieger, was widely recognized as the leading English-language work on the subject. The present volume is not just a revision of the earlier book, but an entirely new presentation, quite different in its axiomatic treatment and inclusion of new material. In particular, this revised edition includes a large number of interesting worked and unworked examples, as well as new discussions of the cardinalities of various sets. In these pages, Professor Sierpiński, a distinguished Polish mathematician, presents a detailed theory of Frechet ( V ) spaces and a comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. The author's exposition is clear and refined; moreover, his axiomatic treatment of the theory of point sets, apart from its logical simplicity, has also an advantage in that it supplies excellent material for exercise in abstract thinking and logical argument in the deduction of theorems from stated suppositions alone; i.e.

, in proving theorems by drawing conclusions according to logic alone, and without any appeal to intuition.