This chapter develops the standard properties of topological spaces. Most of these properties do not go beyond the level of a convenient language. In the text proper, we have given precisely those results which are used very frequently in all analysis. In the exercises, we give additional results, of which some just give routine practice and others give more special results. To incorporate all this material in the text proper would be extremely oppressive and would obscure the principal lines of thought inherent in the basic aspects of the subject. The reader can always be referred to Bourbaki [Bo] or Kelley [Ke] for encyclopaedic treatments.
KeywordsTopological Space Compact Space Open Ball Open Covering Weak Topology
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