A continuous function $f: [0,1] \rightarrow \mathbb{R}$ continuous with $f(0) = f(1)$
12632
Universal Chord Theorem
36150
Ideal in a ring of continuous functions
53627
Proving continuity of $f$
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
34940
Continuity of $f(x) = x^n$
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
18222
Set of continuity points of a real function
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous