Finding a mapping that is not continuous but open
17607
Open maps which are not continuous
61204
Mapping that takes unit circle to unit circle
121957
Is $p\mapsto \|f\|_p$ continuous?
33014
Bijection between an open and a closed interval
27265
Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
65180
A compact Hausdorff space that is not metrizable
61122
A continuous mapping is determined by its values on a dense set
76396
Nowhere monotonic continuous function
108408
Example of quotient mapping that is not open
22641
Nonlinear function continuous but not bounded
15487
Continuous function from a connected set?
91736
Explicit homeomorphism between open and closed rational intervals?
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
103241
A function that is continuous at the origin but not differentiable there
15095
continuous onto map from $(0,1)\to (0,1]$
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
25874
Showing that a certain map is not flat by explicit counterexample