query: Proving that a "nearly entire" continuous function is entire
positive_passages.docid: 13062
positive_passages.text: Which sets are removable for holomorphic functions?
negative_passages.docid: 46514
negative_passages.text: Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 105172
negative_passages.text: Prove that the entire function is constant over certain conditions.
negative_passages.docid: 93021
negative_passages.text: $f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
negative_passages.docid: 41690
negative_passages.text: Products of Continuous functions: Topology
negative_passages.docid: 151427
negative_passages.text: f, g continuous for all rationals follow by continuous on all reals?
negative_passages.docid: 33308
negative_passages.text: Unique local extremum is absolute extremum for continuous functions
negative_passages.docid: 125682
negative_passages.text: Proof verification: the product of two continuous functions is continuous
negative_passages.docid: 12523
negative_passages.text: Supremum of a Continuous Function is Continuous
negative_passages.docid: 118207
negative_passages.text: Prove that the product of two continuous functions is continuous
negative_passages.docid: 15914
negative_passages.text: Prove that any polynomial function is continuous
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 125610
negative_passages.text: Space of bounded continuous functions is complete
negative_passages.docid: 18222
negative_passages.text: Set of continuity points of a real function
negative_passages.docid: 28730
negative_passages.text: product of two uniformly continuous functions is uniformly continuous