Theorem 3.6-2 in Erwine Kreyszig's "Introductory Functional Analysis with Applications:" Does the converse hold if the space is not complete?
47838
Lemma 3.3-7 and Theorem 3.6-2 in Kreyszig's "Introductory Functional Analysis With Applications": What if completeness is lost?
157203
Let $\{f_k\}_{k=1}^\infty\in L^{loc}_1(\mathbb R^n)$, show $\{f_k^2\}_{k=1}^\infty$ does not converge in $\mathscr{D}^\prime(\mathbb R^n)$
26112
Inclusion of $l^p$ space for sequences
46892
Inclusion of $L^p$ spaces
113790
$\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
64619
Continuity of a function of product spaces
149416
Show that $ \{\lnot,\leftrightarrow\} $ is not functional complete
63559
Is there a more complete way of proving this theorem (that I devised)? OR does this theorem already exist and have a name?
124959
Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
12913
space of riemann integrable functions not complete
158353
If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
24478
What is the name of this theorem, and are there any caveats?
143674
Space of bounded functions is complete
100257
Converse to Hilbert basis theorem