02618cam a22002655i 4500001000700000003002100007005001700028008004100045020001800086040002100104082002100125100001400146245005900160260003800219300004600257490003900303504005100342505047000393520130100863650003302164650002402197942001202221999001902233952010002252136640ISI Library, Kolkata20160314164113.0140606s2014 nyu 000 0 eng a9781447164845 aISI Librarybeng04a514.74223bL9171 aLowen, R.10aIndex analysis :bapproach theory at work /cR. Lowen. aLondon :bSpringer-Verlag,c2015. axxi, 466 p. : billustrations ; c25 cm. 0 aSpringer monographs in mathematics aIncludes bibliographical references and index.0 a1. Approach spaces --
2. Topological and metric approach spaces --
3. Approach invariants --
4. Index analysis --
5. Uniform gauge spaces --
6. Extensions of spaces and morphisms --
7. Approach theory meets Topology --
8. Approach theory meets Functional analysis --
9. Approach theory meets Probability --
10. Approach theory meets Hyperspaces --
11. Approach theory meets DCPO?s and Domains --
12. Categorical considerations --
Appendixes --
References --
Index. aIn this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science. 0aIndex theory (Mathematics) 0aTopological spaces. 2ddccBK c420205d420205 00104070aMAINbMAINd2016-03-04g6218.61l1o514.74 L917p136640r2016-05-12s2016-04-13yBK