Find f:R->R such that f(U) is open for all open sets U, but f is not continuous.
17607
Open maps which are not continuous
157603
Continuity $\iff$ Preimage is closed whenever set is closed
64487
Continuous function and dense set
87239
Prove functions defined by sup and inf are continuous
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
22641
Nonlinear function continuous but not bounded
147247
Continuous function on closed unit ball
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
18222
Set of continuity points of a real function
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
98772
Continuity of a function in $\mathbb{R}$
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
15487
Continuous function from a connected set?
62817
Functions which are Continuous, but not Bicontinuous
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?