Elements of Mathematics: General Topology, Pt.1

General Topology - Part I [Bourbaki]......Page cover-1_0001.djvu
Title......Page 0001.djvu
Copyright......Page 0002.djvu
Advice to the Reader......Page 0003.djvu
Contents......Page 0007.djvu
Contents of the Elements of Mathematics Series......Page 0015.djvu
Introduction......Page 0017.djvu
1.1 Open sets, neighborhoods, closed sets......Page 0023.djvu
1.2 Continuous functions......Page 0031.djvu
1.3 Subspaces; quotient spaces......Page 0041.djvu
1.4 Product of topological spaces......Page 0049.djvu
1.5 Open mappings and closed mappings......Page 0056.djvu
1.6 Filters......Page 0063.djvu
1.7 Limits......Page 0074.djvu
1.8 Hausdorff spaces and regular spaces......Page 0081.djvu
1.9 Compact spaces and locally compact spaces......Page 0089.djvu
1.10 Proper mappings......Page 0103.djvu
1.11 Connectedness......Page 0113.djvu
Exercises......Page 0123.djvu
Historical Note......Page 0168.djvu
Bibliography......Page 0173.djvu
2.1 Uniform spaces......Page 0175.djvu
2.2 Uniformly continuous functions......Page 0180.djvu
2.3 Complete spaces......Page 0187.djvu
2.4 Relations between uniform spaces and compact spaces......Page 0204.djvu
Exercises......Page 0212.djvu
Historical Note......Page 0222.djvu
Bibliography......Page 0224.djvu
3.1 Topologies on groups......Page 0225.djvu
3.2 Subgroups, quotient groups, homomorphisms, homogeneous spaces, product groups......Page 0231.djvu
3.3 Uniform structures on groups......Page 0248.djvu
3.4 Groups operating properly on a topological space; compactness in topological groups and spaces with operators......Page 0256.djvu
3.5 Infinite sums in commutative groups......Page 0267.djvu
3.6 Topological groups with operators; topological rings, division rings and fields......Page 0277.djvu
3.7 Inverse limits of topological groups and rings......Page 0290.djvu
Exercises......Page 0302.djvu
Historical Note......Page 0333.djvu
Bibliography......Page 0334.djvu
4.1 Definition of real numbers......Page 0335.djvu
4.2 Fundamental topological properties of the real line......Page 0340.djvu
4.3 The field of real numbers......Page 0345.djvu
4.4 The extended real line......Page 0348.djvu
4.5 Real-valued functions......Page 0353.djvu
4.6 Continuous and semi-continuous real-valued functions......Page 0365.djvu
4.7 Infinite sums and products of real numbers......Page 0369.djvu
4.8 Usual expansions of real numbers; the power of R......Page 0379.djvu
Exercises......Page 0384.djvu
Historical Note......Page 0412.djvu
Bibliography......Page 0423.djvu
Index of Notation......Page 0425.djvu
Index of Terminology......Page 0427.djvu