Is every closed subset the zero set of some smooth function
33734
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
128862
Prove no existing a smooth function satisfying ... related to Morse Theory
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
36315
Is $[0,1]$ a countable disjoint union of closed sets?
67020
Proving that for a smooth function if $f(\frac 1 k)=0 :\forall k\in \mathbb N$ then $f(x)=0 :\forall x\in[-1,1]$
146654
Real valued analytic function defined on a connected set is constant
143586
Is $[0,1]$ a union of family of disjoint closed intervals?
64487
Continuous function and dense set
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
80559
In $C[0,1]$ prove that the subset of Lipschitz functions is dense
84512
The preimage of continuous function on a closed set is closed.
47637
Are strict local minima of a general function always countable?
154621
A set with a finite integral of measure zero?
55374
Cover of (0,1) with no finite subcover & Open sets of compact function spaces
99341
Basic question: closure of irreducible sets
16375
Is the function differentiable at $0$?