Help with proof of continuous functions with neighborhood value $N$.
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
38885
Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
104044
Prove continuous functions $f$ and $g$ are equal
45342
Generalization of Mean Value Theorem to functions, $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$
131992
A problem on continuous functions
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
44574
Continuity of absolute value of a function
40576
Intermediate value property problem and continuous function
147247
Continuous function on closed unit ball
102075
A function continuous on all irrational points
18222
Set of continuity points of a real function
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
64487
Continuous function and dense set
41690
Products of Continuous functions: Topology