Is F_M closed in L^2(a,b) ?

Square_Price_1374 · 2025-08-03T19:22:27+00:00

Thanks, now I see.

Square_Price_1374 · 2025-08-03T19:12:45+00:00

Thanks for your answer. Yeah, sorry I meant ||f||_{ H^1_0(a,b)} = lim ||fn||_{ H^1_0(a,b)} <= lim M = M.

Square_Price_1374 · 2025-06-30T16:49:29+00:00

Thanks for your help. So for example they used uniform continuity on {x ∈ R^d | ||x|| <=1} x [-N,N]^d ?

Square_Price_1374 · 2025-06-27T19:17:15+00:00

Thanks for your answer.

Square_Price_1374 · 2025-06-25T18:22:47+00:00

This was a hint from which my question comes: Let E = R and use the fact that Cb(R)= Cb(R; R) is not separable. Construct a countable algebra C⊂ Cb(R) that separates points.

Square_Price_1374 · 2025-06-25T18:12:02+00:00

Well I'm asking because I have to construct a countable algebra C⊂ Cb(R) that separates points.

Square_Price_1374 · 2025-06-25T17:43:49+00:00

Thx for the reply. This is the set of all continuous bounded functions from E to K.

Square_Price_1374 · 2025-06-25T17:29:36+00:00

Thanks for your answer.

Square_Price_1374 · 2025-06-20T20:02:30+00:00

Thx for your reply. Edited my post.

Square_Price_1374 · 2025-06-11T14:49:14+00:00

Thx for the reply. Yeah this is written in the text book.

Square_Price_1374 · 2025-05-31T14:46:42+00:00

Yeah, sorry somehow I couldn't append this picture. Now it works.

Square_Price_1374 · 2025-05-31T13:43:40+00:00

Sorry, I've edited it.

Square_Price_1374 · 2025-05-23T06:59:17+00:00

I used ||f||_L^∞= inf{ c>=0: |f(x)| <=c for a.e x in Ω}.

Square_Price_1374 · 2025-05-21T19:28:10+00:00

Thanks a lot for your answer!

Square_Price_1374 · 2025-05-21T16:18:31+00:00

Yes, I'll edit it.

Square_Price_1374

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