Showing a function is continuous and analytic
38885
Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
106175
A function is analytic if and only if it is holomorphic
102075
A function continuous on all irrational points
64748
analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence
15914
Prove that any polynomial function is continuous
153855
Complex analysis, showing a function is constant
110112
Proving a function is Lipschitz continuous
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
50342
Proving that a Function is Analytic Given that it is Equal to the Complex Conjugate of an analytic Function
100979
Uniform continuity of a function and cauchy sequences
71487
Real Analysis: Continuity of a Composition Function
17234
Show that a continuous function has a fixed point
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
8039
an analytic function from unit disk to unit disk with two fixed point