Categorical Topology: Proceedings Of The International Conference, Berlin, August 27th To September 2nd 1978 (lecture Notes In Mathematics)

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previous edition: "The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities." —Physics Today "Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done." —Zentralblatt MATH Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previous edition: "The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities."--Physics Today "Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background) ... The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.) ... Summarizing: Well done." --Zentralblatt MATH Recovering a space from its banach sheaves....Pages 1-12 Completeness is productive....Pages 13-17 Legitimacy of certain topological completions....Pages 18-23 On E-normal spaces....Pages 24-34 Two procedures in bitopology....Pages 35-43 Saks spaces and vector valued measures....Pages 44-54 A question in categorical shape theory: When is a shape-invariant functor a kan extension?....Pages 55-62 The finest functor preserving the baire sets....Pages 63-73 Lifting closed and monoidal structures along semitopological functors....Pages 74-83 On non-simplicity of topological categories....Pages 84-93 Kan Lift-extensions in C.G. Haus....Pages 94-101 Topological functors from factorization....Pages 102-111 Groupoids and classification sequences....Pages 112-121 Concentrated nearness spaces....Pages 122-136 Initial and final completions....Pages 137-149 Algebra ∪ topology....Pages 150-156 Topological spaces admitting a "Dual"....Pages 157-166 Special classes of compact spaces....Pages 167-175 Pairs of topologies with same family of continuous self-maps....Pages 176-184 Hereditarily locally compact separable spaces....Pages 185-195 Injectives in topoi, I: Representing coalgebras as algebras....Pages 196-206 Injectives in Topoi, II: Connections with the axiom of choice....Pages 207-216 Categories of statistic-metric spaces....Pages 217-224 A categorical approach to primary and secondary operations in topology....Pages 225-233 Limit-metrizability of limit spaces and uniform limit spaces....Pages 234-242 Banach spaces over a compact space....Pages 243-249 A note on (E,M)-functors....Pages 250-258 Convenient topological algebra and reflexive objects....Pages 259-276 Existence and applications of monoidally closed structures in topological categories....Pages 277-292 Connection properties in topological categories and related topics....Pages 293-307 On projective and injective objects in some topological categories....Pages 308-315 An embedding characterization of compact spaces....Pages 316-325 Connection and disconnection....Pages 326-344 Connections between convergence and nearness....Pages 345-357 Functors on categories of ordered topological spaces....Pages 358-370 On the coproduct of the topological groups Q and Z 2 ....Pages 371-375 Lifting semifinal liftings....Pages 376-385 Normally supercompact spaces and convexity preserving maps....Pages 386-394 Structure Functors....Pages 395-410 Function spaces in topological categories....Pages 411-420 Beginning with reviews of vector algebra and differential and integral calculus, this book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations