Show function is continuous for all x and y
100187
Show function is continuous at origin
57180
Techniques to prove a function is uniformly continuous
17234
Show that a continuous function has a fixed point
125682
Proof verification: the product of two continuous functions is continuous
49099
Constructing a continuous function whose graph seems 'special'
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
15487
Continuous function from a connected set?
126212
Proving uniform continuity on an interval
15690
Is a function defined at a single point continuous?
23294
Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
134752
Proof (epsilon delta) for the continuity of a function at a point
137043
To show that function is constant
24817
Prove continuity on a function at every irrational point and discontinuity at every rational point.
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
87239
Prove functions defined by sup and inf are continuous
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?