Function whose image of every open interval is $(-\infty,\infty)$
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
19072
$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
126212
Proving uniform continuity on an interval
70264
Prove that the inverse image of an open set is open
91736
Explicit homeomorphism between open and closed rational intervals?
62817
Functions which are Continuous, but not Bicontinuous
102075
A function continuous on all irrational points
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
65346
Characterisation of uniformly continuous function
124916
$f$ such that $\int_1^{\infty}f(x)dx$ converges, but not absolutely?
124861
The extension of smooth function
6417
Can a function be differentiable at the end points of its (closed interval) domain?
15487
Continuous function from a connected set?
69283
The limit points of an open interval (open set)
11586
Sequences of Real Numbers in a closed bounded interval
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
126259
Minimum of a function on an open interval