query: A Bounded Continuous Function on a Circle
positive_passages.docid: 143000
positive_passages.text: Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
negative_passages.docid: 41847
negative_passages.text: Uniformly continuous function with unbounded variation
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 113122
negative_passages.text: Prove that a continuous real function with finite limits is bounded
negative_passages.docid: 55749
negative_passages.text: Compactly supported continuous function is uniformly continuous
negative_passages.docid: 74245
negative_passages.text: Characterizing non-constant entire functions with modulus $1$ on the unit circle
negative_passages.docid: 75479
negative_passages.text: Proving that this function is continuous on $G\times G$
negative_passages.docid: 9451
negative_passages.text: Show bounded and convex function on $\mathbb R$ is constant
negative_passages.docid: 126759
negative_passages.text: Unbounded continuous function on non-compact metric space
negative_passages.docid: 32789
negative_passages.text: Show bounded harmonic function on $\mathbb{C}$ is constant.
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 124535
negative_passages.text: continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
negative_passages.docid: 75735
negative_passages.text: Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
negative_passages.docid: 47419
negative_passages.text: Asymptotics of uniformly continuous functions over $\mathbb R$
negative_passages.docid: 115878
negative_passages.text: Continuous unbounded but integrable functions
negative_passages.docid: 47188
negative_passages.text: Uniformly Continuous Function sending Bounded Set to Unbounded One
negative_passages.docid: 70645
negative_passages.text: Borel set preserved by continuous map