Can $f$ ever has uncountable number of Local maxima or minima?
55679
Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
79490
Proving the set of points at which a function diverges to $\infty$ is countable
22294
Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
9748
Maximum modulus principle for an unbounded function in the half right plane
76249
Does the limit of function of two variables exist
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
136106
Is every open subset of $ \mathbb{R} $ uncountable?
31522
Proving $f$ has at least one zero inside unit disk
75882
Countability of local maxima on continuous real-valued functions
24837
$x^2+1=0$ uncountable many solutions
43419
At unique critical point, does local max imply global max?
39351
$f(X)$ is uncountable and hence $X$ is uncountable.
28191
How to show that a set of discontinuous points of an increasing function is at most countable
14972
Cardinality of Vitali sets: countably or uncountably infinite?
57785
Finding all maxima and minima of a function
79925
Infinitely many values of $x$ that satisfy the equations
22391
Is the set of all pairs of real numbers uncountable?