Stereotype space | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Stereotype_space


00:00:56 1 Definition
00:04:28 2 Examples
00:13:43 3 History
00:14:37 4 Pseudocompletion and pseudosaturation
00:22:37 5 Immediate subspaces and immediate quotient spaces
00:23:02 5.1 Immediate subspaces and envelopes
00:35:55 5.2 Immediate quotient spaces and refinements
00:50:13 6 Category bSte/b of stereotype spaces
00:51:07 6.1 Kernel and cokernel in the category bSte/b
00:56:32 6.2 bSte/b as a *-autonomous category
01:03:07 6.3 Limits and colimits in the category bSte/b
01:16:35 6.4 Grothendieck transformation
01:22:08 6.5 Stereotype approximation property
01:27:32 7 Applications
01:36:46 8 See also
01:40:16 9 Notes
01:40:53 10 External links
01:41:03 11 References



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SUMMARY
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In functional analysis and related areas of mathematics, stereotype spaces are topological vector spaces defined by a special variant of reflexivity condition. They form a class of spaces with a series of remarkable properties, in particular, this class is very wide (for instance, it contains all Fréchet spaces and thus, all Banach spaces), it consists of spaces satisfying a natural condition of completeness, and it forms a *-autonomous category with the standard analytical tools for constructing new spaces, like taking dual space, space of operators, tensor products, and in addition, immediate subspace, immediate quotient space, products and coproducts, limits and colimits, etc.