Talk:Kuratowski convergence
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Additional example
[edit]I would like to add some additional examples, but I am not sure if these exmaples are correct:
- Let Cn be a sequence of circles with center at (0,0) and radius R+1/n, for some constant R>=0. Then Cn converges to a circle with center at (0,0) and radius R (if R>0), or to the point (0,0) (if R=0).
- Let S be a constant 2-dimensional geometric shape. Let Tn be a sequence of 5-tuples that converges to (0,0,1,1,0). For every n, let Sn be the shape S translated horizontally by Tn1, translated vertically by Tn2, scaled horizontally by Tn3, scaled vertically by Tn4 and rotated by Tn5. Then the sequence Sn converges to S (this is a generalization of the previous example).
Is this correct? --Erel Segal (talk) 06:08, 4 March 2014 (UTC)
Small correction
[edit]"Kuratowski convergence coincides with convergence in Fell topology."
Only for sequences (Beer's book, page 147). At the beginning of the article it is stated that Kuratowski convergence is also a mode of convergence for nets, which introduces a potential misinterpretation here.--93.156.35.197 (talk) 14:39, 31 December 2014 (UTC)
Major rewrite and expansion
[edit]I just added a large quantity of new content for this page. Revisions welcomed! InfCompact (talk) 22:50, 22 December 2022 (UTC)