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| | Department of Mathematics, University of Strathclyde |
 | | To introduce and study the basic ideas of topological vector spaces which are important in applications. |
 | | Basic ideas of topology: open sets, closed sets, bases; interior, closure; denseness and separability; subspaces, induced topology; product spaces; separation; continuity; homeomorphism. |
 | | Topological vector spaces: continuity of the algebraic operations, base of neighbourhoods of the origin; convexity, locally convex spaces, seminorms, metrizability; duality, Hahn-Banach theorem, weak topology, bounded sets, polar sets, polar topologies; precompactness, compactness, completeness; Mackey-Arens theorem; inductive and projective limits: quotients, direct sums and products; some special classes of spaces. |
| www.maths.strath.ac.uk /ungrad/classes/516.htm (190 words) |
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