Are connectedness preserving monotone functions continuous?
73559
Map preserving intervals but discontinuous
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
17223
Continuity of an inverse function.
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
64619
Continuity of a function of product spaces
58816
Existence of a continuous function which does not achieve a maximum.
83461
Continuous iff composition with every linear functional is continuous
28315
Monotone functions and non-vanishing of derivative
142232
Functional Analysis. Continuous extensions of linear functionals.
60521
Continuity of a convex function
75882
Countability of local maxima on continuous real-valued functions
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
152877
Is a monotone differentiable function continuously differentiable?
63598
Is every separately continuous function on $R^2$ continuous?
64487
Continuous function and dense set
60700
Continuity of a function to the integers
59859
Locally Lipschitz implies continuity. Does the converse implication hold?