There is any smooth function on real line which is zero just in [0,1]
33734
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
18222
Set of continuity points of a real function
155871
Is it possible for a function to be smooth everywhere, analytic nowhere, yet Taylor series at any point converges in a nonzero radius?
64836
Functions that are always less than their derivatives
18611
An analytic function with a simple pole
69845
Construct a real function with is exactly $C^2$ such that its first derivative does not vanish everywhere
131000
A proof of a criterion of vanishing of a function.
54137
Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable
126017
Entire function having simple zero at the Gaussian integers
40014
A polynomial that is zero on an open set
55679
Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
12639
Example of primitive function which isn't Riemann-integrable on a closed interval [0,1]
91304
An entire function whose integral is bounded is identically zero
134199
Holomorphic function mapping a set onto a straight line
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
5625
Entire function with vanishing derivatives?
7861
Non-analytic smooth function