Uncertainty principle - Duration bandwidth principle
An important  theorem, known as Weyl's, 1931, is:
if  function $s(t)$ and  related functions $ts(t)$, $s'(t)$ are in $L^2$ (square integrable) with the related $\|\cdot\|$ $L_2$ norm symbol then:
$$ \| s(t) \|^2 \leq 2\| ts(t) \| \| s'(t) \|$$
Equality is attained when  $s(t)$ is a modulated Gaussian/Gabor elementary function defined as:
$$ s'(t) / s(t)  \propto t $$
or practically as:
$$s(t) = C \exp [-\alpha(t - t_m)^2 + \imath 2 \pi \nu_m (t - t_m)]$$
found by integration by part + Cauchy–Bunyakovsky–Schwarz.
If one defines  time or frequency location, as a center of mass related to energy as:
$$ E = \int |s(t)|^2 dt = \int |S(f)|^2 df$$
and
$$\overline{t} = 1/E \int t|s(t)|^2 dt \qquad \overline{f} = 1/E \int f|S(f)|^2 df$$
and  energy dispersion as:
$$\Delta t = \sqrt{1/E \int (t - \overline{t})^2 |s(t)|^2 dt }$$
$$\Delta f = \sqrt{1/E \int (f - \overline{f})^2 |S(f)|^2 df }$$
then for  finite-energy every signal  $s(t)$,  with $\Delta t$  and $\Delta f$ finite, one gets:
$$\Delta t\Delta f \geq \frac{1}{4\pi}$$
The limit is attained for some Gaussian variations. My interpretation of the question is is more about the term 'time/frequency dispersion' than the fuzzy concept of 'time/frequency resolution'.