Continuity of a function $f:X \longrightarrow Y$ Where $X,Y$ metric space
12997
Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
143174
property of continuous function
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
76351
Equivalence of continuity definitions
100187
Show function is continuous at origin
60521
Continuity of a convex function
53738
Monotone functions and continuity
60070
Unique uniformly continuous function into complete space
10747
Given function $g$ continuous in line $[0,\infty)$...
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
12523
Supremum of a Continuous Function is Continuous
32571
Is the maximum function of a continuous function continuous?
126842
Fixed point in a continuous function
45581
Is the distance function in a metric space (uniformly) continuous?
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
34940
Continuity of $f(x) = x^n$