$f:\Bbb R\to \Bbb R$ be a continuous function such that $f(i)=0\forall i\in \Bbb Z$
119060
What can you say about a continuous function that is zero at all integer values?
47419
Asymptotics of uniformly continuous functions over $\mathbb R$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
149328
A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020)
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
53726
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
154521
Linear functional $f$ is continuous at $x_0=0$ if and only if $f$ is continuous $\forall x\in X$?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous