Problem regarding proving a real valued function to be continuous.
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
155170
Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition
126212
Proving uniform continuity on an interval
80872
Remark from baby Rudin about continuous function
75479
Proving that this function is continuous on $G\times G$
125682
Proof verification: the product of two continuous functions is continuous
139763
A function takes every function value twice - proof it is not continuous
71487
Real Analysis: Continuity of a Composition Function
117502
Proving that a certain continuous function is surjective.
64619
Continuity of a function of product spaces
113122
Prove that a continuous real function with finite limits is bounded
12349
a construction of a continuous function from a normal space to [0,1]
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
53627
Proving continuity of $f$
52380
How to prove the function $e^x$ is continous for all real numbers
136011
Must $f$ be continuous?
727
Prove that any continuous integer-valued function of a real variable is constant.