Proof explanation: Hahn-Banach Theorem in Stein's functional analysis
139367
Hahn Banach Theorem: Transfinite Induction
2677
Baire: Show that $f\colon \mathbb{R}\to\mathbb{R}$ is a polynomial in an open bounded set
81112
Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
29836
Prove: Convergent sequences are bounded
156161
Banach-Tarski theorem without axiom of choice
144656
Linear functional and a bounded norm
104607
Hahn-Banach theorem, dual space
48804
Enumeration of rationals from Stein-Shakarchi's Real Analysis (Chapter 1, Exercise 24)
140813
How do i prove that continuous linear transformation between normed spaces is bounded?
115781
Proof about Holomorphic functions in the unit disc
77283
Cauchy functional inequality
71001
Do continuous linear functions between Banach spaces extend?
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
28731
Banach space in functional analysis
34865
prove Eckart-Young-Minsky theorem for Frobinius norm.
103606
Proof of sandwich/squeeze theorem for series.
47838
Lemma 3.3-7 and Theorem 3.6-2 in Kreyszig's "Introductory Functional Analysis With Applications": What if completeness is lost?