10-327/Homework Assignment 8 Solutions - Revision history

Xwbdsb at 22:53, 19 December 2010

2010-12-19T22:53:04Z

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	I think the set of homeworks is a finite point set, hence automatically compact ... if you view the homeworks as spaces instead of points, then the resulting product space is complete if each homework is complete, as we know ... exercise: (a) is the converse also true? (b) what about infinite products?		I think the set of homeworks is a finite point set, hence automatically compact ... if you view the homeworks as spaces instead of points, then the resulting product space is complete if each homework is complete, as we know ... exercise: (a) is the converse also true? (b) what about infinite products?

			-The resulting product space is complete only if you put that weird metric that induces the product topology. When the space is not metric we cannot talk about completeness. Converse depends on what kind of metric you define on the projection? countable infinite product is done in the book. It is complete with that weird metric induced from metrics from all the spaces.-Kai

	Anyway, here is another solution set, this one typed (though not graded, so use at your own risk): [[User:Bcd\|Bcd]] 14:40, 19 December 2010 (EST)		Anyway, here is another solution set, this one typed (though not graded, so use at your own risk): [[User:Bcd\|Bcd]] 14:40, 19 December 2010 (EST)

Bcd at 19:40, 19 December 2010

2010-12-19T19:40:03Z

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	-Kai [[User:Xwbdsb\|Xwbdsb]] 07:32, 19 December 2010 (EST)		-Kai [[User:Xwbdsb\|Xwbdsb]] 07:32, 19 December 2010 (EST)

			I think the set of homeworks is a finite point set, hence automatically compact ... if you view the homeworks as spaces instead of points, then the resulting product space is complete if each homework is complete, as we know ... exercise: (a) is the converse also true? (b) what about infinite products?

			Anyway, here is another solution set, this one typed (though not graded, so use at your own risk): [[User:Bcd\|Bcd]] 14:40, 19 December 2010 (EST)

			[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:10-327-HW8.pdf]

Xwbdsb at 12:32, 19 December 2010

2010-12-19T12:32:51Z

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			In order to make our topological space of homework assignments complete, I need to upload the solution to the last assignment.(Sorry for getting so busy and keep forgetting things) What metric we should put on it?...Its quite difficult to create a complete space...

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			-Kai [[User:Xwbdsb\|Xwbdsb]] 07:32, 19 December 2010 (EST)

Anne.d at 02:59, 11 December 2010

2010-12-11T02:59:42Z

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