Continuous injection of $[a,b]$ is strictly monotonic from Zorich's book
20284
Continuous injective map is strictly monotonic
72642
Continuous bijection from $(a,b) \to S^1$?
141366
Absolutely continuity and Lipschitz-like continuity
65033
Prove inverse of strictly monotone increasing function is continuous over the range of original function
158349
Prove the map sending a matrix to it's inverse is continuous.
117502
Proving that a certain continuous function is surjective.
14489
Showing that a sequence is monotone and thus convergent
12349
a construction of a continuous function from a normal space to [0,1]
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
141895
Proving that a sequence is monotone
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
32359
Inner product of two continuous maps is continuous
125682
Proof verification: the product of two continuous functions is continuous
76396
Nowhere monotonic continuous function
106799
Proof Verification: Converse of Intermediate Value Theorem
153580
Solutions of autonomous ODEs are monotonic
146306
A continuous surjective function from $(0,1]$ onto $[0,1]$