Prove that $f \ast g$ is continuous and bounded if $f\in L^1(R^n)$ and $g\in L^\propto (R^n)$
117528
$f$ is bounded and continious $\Rightarrow$ the convolution integral $\int f(\tau)g(x-\tau)\text{ d}\tau$ is bounded and continuous
49438
Prove that $X^\ast$ separable implies $X$ separable
106531
A Fourier transform of a continuous $L^1$ function
66691
Real function continuous on closed interval implies it is bounded - over-simple proof??
145368
How to show $f:Y\to X^{+}$ is continuous?
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
142014
study of subspace generated by $f_k(x)=f(x+k)$ with f continuous, bounded..
53627
Proving continuity of $f$
76607
Show that exists a continuous function in $E$ that is not bounded
131992
A problem on continuous functions
117502
Proving that a certain continuous function is surjective.
125610
Space of bounded continuous functions is complete
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
127739
Is a continuous function on a bounded set bounded itself?
2118
Are continuous functions with compact support bounded?
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed