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 Mar 1 awarded Yearling Oct 7 awarded Popular Question Oct 5 awarded Popular Question May 20 comment Is the “product rule” for the boundary of a Cartesian product of closed sets an accident? @CameronWilliams. I tried, but had no luck. Thank you all the same. May 20 comment Is the “product rule” for the boundary of a Cartesian product of closed sets an accident? Hi, @CameronWilliams, would you please point out a reference to this result? Thanks a lot. Mar 31 awarded Tumbleweed Mar 24 comment Are these equivalent definitions of faces of convex sets? @timhortons Thanks a lot. Mar 23 revised Are these equivalent definitions of faces of convex sets? added 3 characters in body Mar 23 revised Are these equivalent definitions of faces of convex sets? added 2 characters in body Mar 23 asked Are these equivalent definitions of faces of convex sets? Mar 23 asked Are these inconsistent definitions of extreme subset of convex set? Oct 3 comment Will continuous extension preserve strict convexity? This function is not even convex. You can consider $g(x)=h(x,x)=(x^2-1)^2$. Oct 3 asked Will continuous extension preserve strict convexity? Sep 21 accepted Is the limit point of this sequence unique? Sep 21 comment Is the limit point of this sequence unique? Great. I'd better pick up a book and review some basics. Sep 21 comment Is the limit point of this sequence unique? Thanks for your quick response. Please see my edit. Sep 21 revised Is the limit point of this sequence unique? added 48 characters in body Sep 21 asked Is the limit point of this sequence unique? Sep 15 comment normal cone to sublevel set Without the assumption that ${\rm cone}\,\partial f(\bar{x})$ is closed, why is the inclusion $N_C(\bar{x})\subset{\rm cone}\,\partial f(\bar{x})$ equivalent to $(N_C(\bar{x}))^{\circ}\supset({\rm cone}\,\partial f(\bar{x}))^{\circ}$? Sep 15 comment normal cone to sublevel set This is indeed an exercise in Borwein's book: Convex analysis and nonlinear optimization. Although it is an exercise, I think it is very useful to relate many stuff together. As I mentioned, it appears in many other textbooks as a theorem in a bit different form.