query: Prove that $f$ is a non const continuous map then the image of an uncountable set under the map is uncountable.
positive_passages.docid: 154474
positive_passages.text: Image of countable and uncountable sets
negative_passages.docid: 83326
negative_passages.text: $f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
negative_passages.docid: 139744
negative_passages.text: For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
negative_passages.docid: 41690
negative_passages.text: Products of Continuous functions: Topology
negative_passages.docid: 97761
negative_passages.text: Show that a proper continuous map from $X$ to locally compact $Y$ is closed
negative_passages.docid: 14896
negative_passages.text: Prove: the set of zeros of a continuous function is closed.
negative_passages.docid: 113975
negative_passages.text: Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
negative_passages.docid: 70645
negative_passages.text: Borel set preserved by continuous map
negative_passages.docid: 94781
negative_passages.text: Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
negative_passages.docid: 70264
negative_passages.text: Prove that the inverse image of an open set is open
negative_passages.docid: 111485
negative_passages.text: Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
negative_passages.docid: 88586
negative_passages.text: show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant
negative_passages.docid: 29582
negative_passages.text: Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
negative_passages.docid: 100740
negative_passages.text: proof of that a continuous function has a fixed point
negative_passages.docid: 55238
negative_passages.text: Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
negative_passages.docid: 72044
negative_passages.text: prove $x \mapsto x^2$ is continuous
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal