Continuous at a point
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
88640
Is $\sqrt x$ continuous at $0$? Because it is not defined to the left of $0$
12349
a construction of a continuous function from a normal space to [0,1]
101593
Possible to have a continuous sequence?
136011
Must $f$ be continuous?
17234
Show that a continuous function has a fixed point
22641
Nonlinear function continuous but not bounded
91682
Graph of a continuous function is closed
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
71487
Real Analysis: Continuity of a Composition Function
46642
Continuity of $\sin(x)/x$
65346
Characterisation of uniformly continuous function
15487
Continuous function from a connected set?
147247
Continuous function on closed unit ball
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
18222
Set of continuity points of a real function