prove that a non constant linear functional from a normed linear space X is discontinuous if and only if Z(f) = {x in X | f(x) = 0} is dense in X.
130586
$f$ is discontinuous $\iff$ kernel($f$) is dense in X
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
64619
Continuity of a function of product spaces
28731
Banach space in functional analysis
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?
57839
Real analysis: density and continuity
88240
Two functions discontinuous, but sum continuous
24900
Homogeneity and Differentiability at $0$ implies linearity?
152563
Set of discontinuity of monotone function is countable
83023
From axiom of regularity, how can I prove $x \notin y \lor y \notin x$
64487
Continuous function and dense set
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
38886
Discontinuous function on Q
142232
Functional Analysis. Continuous extensions of linear functionals.
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
119947
Can a non-zero vector have zero image under every linear functional?
43001
Proof for Dirichlet Function and discontinuous