Topology of uniform convergence | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-06

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Topology_of_uniform_convergence


00:00:27 1 Topologies of uniform convergence
00:08:36 2 Spaces of continuous linear maps
00:10:32 2.1 Properties
00:10:41 2.1.1 Completeness
00:12:23 2.1.2 Boundedness
00:15:06 2.2 Examples
00:15:15 2.2.1 The topology of pointwise convergence iL/isubi&#963;/i/sub(iX/i, iY/i)
00:17:34 2.2.2 Compact-convex convergence iL/isubi&#947;/i/sub(iX/i, iY/i)
00:18:18 2.2.3 Compact convergence iL/isubic/i/sub(iX/i, iY/i)
00:20:12 2.2.4 Strong dual topology iL/isubib/i/sub(iX/i, iY/i)
00:21:49 3 G-topologies on the continuous dual induced by iX/i
00:33:25 3.1 Examples
00:33:34 3.1.1 The weak topology iσ/i(iX/isup*/sup, iX/i) or the weak* topology
00:39:56 3.1.2 Compact-convex convergence iγ/i(iX/isup*/sup, iX/i)
00:41:32 3.1.3 Compact convergence ic/i(iX/isup*/sup, iX/i)
00:43:43 3.1.4 Precompact convergence
00:44:45 3.1.5 Mackey topology iτ/i(iX/isup*/sup, iX/i)
00:45:57 3.1.6 Strong dual topology ib/i(iX/isup*/sup, iX/i)
00:52:00 3.1.7 Mackey topology iτ/i(iX/isup*/sup, iX/isup**/sup)
00:54:04 3.1.8 Other examples
00:54:40 4 G-topologies on iX/i induced by the continuous dual
00:58:10 4.1 Examples
00:58:19 4.1.1 The weak topology i&#963;/i(iX/i, iX/isup*/sup)
01:00:39 4.1.2 Convergence on equicontinuous sets i&#949;/i(iX/i, iX/isup*/sup)
01:02:22 4.1.3 Mackey topology i&#964;/i(iX/i, iX/isup*/sup)
01:03:55 4.1.4 Bounded convergence ib/i(iX/i, iX/isup*/sup)
01:05:07 4.2 The Mackey–Arens theorem
01:07:41 5 G-H-topologies on spaces of bilinear maps
01:15:35 5.1 The iε/i-topology
01:22:31 6 See also



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SUMMARY
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In mathematics, a linear map is a mapping V → W between two modules (including vector spaces) that preserves the operations of addition and scalar multiplication.
By studying the linear maps between two modules one can gain insight into their structures. If the modules have additional structure, like topologies or bornologies, then one can study the subspace of linear maps that preserve this structure.