* [[Thomae'sBlumberg functiontheorem]] (alsostates knownthat aseven theif popcorna real function)—''f'' a: functionℝ that→ ℝ is nowhere continuous, atit allexists irrationala numbersdense andsubset discontinuous''D'' atof allℝ rationalsuch numbersthat the restriction of ''f'' to ''D'' is continuous.
* [[WeierstrassThomae's function]]:A(also known as the popcorn function) — a function that is ''continuous''everywhereat (insideall itsirrational ___domain)numbers and ''differentiable''discontinuous at all rational nowherenumbers.
* [[Weierstrass function]]: A function ''continuous'' everywhere (inside its ___domain) and ''differentiable'' nowhere.
