# User talk:Mgkrupa

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## January 2014

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• sigma})^*[/itex]). In fact, this canonical map is ''onto'', which means that $X = X^*_{\sigma})^*$ so that we can through this canonical isomorphism think of ''X'' as the continuous dual

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## Topologies of uniform convergence

I think the title of your new article Topologies of uniform convergence might be too general. The article treats only the case of topological vector spaces, but the notion of uniform convergence makes sense in any uniform space. Perhaps Uniform convergence in a topological vector space (or similar) would be a better title? Sławomir Biały (talk) 13:29, 26 January 2014 (UTC)

How about Topologies of uniform convergence on spaces of linear maps? Sławomir Biały (talk) 23:39, 26 January 2014 (UTC)
That's not accurate however since, for instance, this construction is also used for bilinear maps and this name would exclude this set of maps (since the only map that is both linear and bilinear is the 0 map)Mgkrupa (talk) 00:36, 27 January 2014 (UTC)
There is a suggestion at WT:WPM to merge with Polar topology. Sławomir Biały (talk) 13:06, 27 January 2014 (UTC)

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## Commutative Diagram Example

I realize it's been some time since you added the example here, and I certainly understand you have no obligation to respond, but if you're willing, I had hoped you might clarify why, in the third example you provided, "it is generally not enough to only have equalities (1) and (2)" for the diagram to commute.

Specifically, it seems I can derive equality (3) from equalities (1) and (2) by showing that rhg = HGl = Hmg and eliminating g by epimorphism, leaving rh = Hm, as desired.

This is not my area of expertise, but if you would be so generous as to even cite a source for the examples, I will happily correct my intuition and supplement the article for my own sake.

Hi Absemindprof and thank you for your message. If g had been an epimorphism then that would work but no assumptions were made about any of the objects or morphisms in that example. I guess that point should be emphasized. A counter example in the category of sets is ${\displaystyle A=D=\emptyset }$, ${\displaystyle B=C=E=\{0\}}$, ${\displaystyle F=\{0,1\}}$, ${\displaystyle l,m,g,G,h}$ being the only possible maps, and ${\displaystyle r}$ (resp. ${\displaystyle H}$) sending its only element to ${\displaystyle 0}$ (resp. ${\displaystyle 1}$). Feel free to include this example in that article if you want. Best wishes. Mgkrupa (talk) 01:30, 9 October 2016 (UTC)