query: let $f$ be a entire function and $B$ is bounded open set. $\partial(f(B)) \subset f(\partial B)$.
positive_passages.docid: 89205
positive_passages.text: Image under an entire function.
negative_passages.docid: 73130
negative_passages.text: A simple question about open set
negative_passages.docid: 98151
negative_passages.text: Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.
negative_passages.docid: 127739
negative_passages.text: Is a continuous function on a bounded set bounded itself?
negative_passages.docid: 34542
negative_passages.text: If $f$ is integrable then $|f|$ is also integrable
negative_passages.docid: 111538
negative_passages.text: If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
negative_passages.docid: 1954
negative_passages.text: Entire function bounded by polynomial of degree 3/2 must be linear.
negative_passages.docid: 143105
negative_passages.text: Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
negative_passages.docid: 7755
negative_passages.text: Question on entire function
negative_passages.docid: 63255
negative_passages.text: Proving an entire, complex function with below bounded modulus is constant.
negative_passages.docid: 72468
negative_passages.text: Open and closed balls in $C[a,b]$
negative_passages.docid: 147270
negative_passages.text: Entire function. Prove that $f(\bar{z})=\overline{f(z)}, \forall z\in C$
negative_passages.docid: 79697
negative_passages.text: If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
negative_passages.docid: 116064
negative_passages.text: Does every holomorphic function $f$ defined on an open set $U$ have a primitive?
negative_passages.docid: 142459
negative_passages.text: Continuity of a Function in Terms of Closure and Interior
negative_passages.docid: 84206
negative_passages.text: How do I show that if $f$ is entire and $\{\lvert f(z)\rvert < M\}$ is connected for all $M$, then $f$ is a power function?
negative_passages.docid: 76285
negative_passages.text: Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.