Topology of Metric Spaces"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET. |
Contents
Basic Notions | 1 |
2 | 16 |
91 | 32 |
Continuity | 61 |
Compactness | 81 |
Connectedness | 113 |
Complete Metric Spaces | 122 |
Bibliography | 149 |
Common terms and phrases
admit a finite arbitrary topological space Archimedean property Assume bijection Cauchy sequence choose claim closed sets closed subset cluster point compact metric space compact subset conclude connected subset Consider constant continuity of ƒ continuous function contradiction convergent sequence convergent subsequence countable d(xm d(xn dA(x define Definition denote dense sets equivalent Example f(xn Figure finite subcover fn(x function f ƒ is continuous geometric given ɛ Hausdorff Hence Hint homeomorphic iff there exists induced metric infinite inner product intersection isometry J₁ Lemma Let f limit point open ball open cover open set path connected product metric prove reader real numbers result sequence fn Show that ƒ subset of R2 sup norm topological space totally bounded triangle inequality uniformly continuous uniformly equicontinuous union upper bound vector space მყ