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What does the sentence mean: "Convergence in this topology (uniform norm topology) is uniform convergence of the functions" ? (Gillman, Jerison : Rings of Continuous Functions) Does it mean whenever a sequence of functions on the said space…Continue
Started this discussion. Last reply by E Krishnan Apr 4, 2012.
I would like to read some detailed disscussion on Uniform Norm Topology & m-topology. Can anyone suggest some standard texts/lecture notes? ("GILLMAN/JERISON: Rings of Continuous. Functions" was found to be a little bit compact for me.)Continue
Tags: m-topology, Topology, Norm, Uniform
Started this discussion. Last reply by Amber Habib Apr 14, 2012.
Let (X, d) be a compact metric space. Suppose that f: X ---> X is a function such that d(f(x), f(y)) < d(x, y) for x ≠ y; x, y Є X. Then show that there exists x' Є X such that f(x') = x'.Continue
Started this discussion. Last reply by Amber Habib Apr 14, 2012.
Speaking at the annual convention of the American Federation of Teachers recently, Bill talked about the importance of developing more effective ways to measure teaching excellence and share best practices to improve education in the classroom.
When you think about it, teaching is one of the most difficult, complex professions there is. You have to be able to make a subject clear, and interesting. You have to calm the disruptive kids, challenge the advanced kids,…
ContinuePosted on June 22, 2011 at 9:02pm
There is a philosophical doctrine known as bialetheism, with, apparently, many adherents in Australia, who take the view that there can be true contradictions. I do not wish to defend this view, but nevertheless in the next 45 minutes I will be arguing, sincerely, that mathematics both does and does not need a philosophy. Of course, the apparent contradiction can in my case be resolved in a boringly conventional way: the statement "Mathematics needs philosophy" has…
ContinuePosted on June 21, 2011 at 11:08am
In the May 2011 issue of Scientific American mathematician John Baez co-authors "The Strangest Numbers in String Theory," an article about the octonions, an eight-dimensional number system that was discovered in the mid–19th century but that has been largely ignored until quite recently. As the name of the article implies, interest in the octonions has been rekindled…
ContinuePosted on June 18, 2011 at 7:26am
Now that the project to upgrade my old multiple choice applet to a more modern and collaborative format is underway (see this server-side demo and this javascript/wiki demo, as well as the …
ContinuePosted on June 16, 2011 at 6:25pm
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