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addition arbitrary Assume bounded called cardinal number centralized Chap choose clopen closed set compact compact space compactum completely regular space condition connected Consequently Consider consists constructed containing continuous function continuous mapping contradiction converges countable base defined definition denote dense discrete disjoint element equality example exists extension extremally disconnected fact follows function given Hausdorff space Hence homeomorphic implies induction infinite intersection interval irreducible limit Lindelof locally compact locally finite maximal metric space natural nhood nonempty normal space obtain Obviously one-to-one open cover open set ordered pair paracompact perfect mapping preceding problem Prob proof prove refinement relation respect satisfying separable sequence Show solution space X statement subset Suppose topological space topology union usual weight well-ordered
Page 11 - As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection.
Page 11 - Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years:...
Page 11 - ... into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another. The Mathematics and Its Applications programme tries to make available a careful selection of books which fit the philosophy outlined above. With such books, which are stimulating rather than definitive, intriguing rather than encyclopaedic, we hope to contribute something towards better communication among the practitioners in diversified fields.