query: There exist no continuous one one onto (Bijective ) function form $[0,1]$ $\to$ $[0,1]\times[0,1]$
positive_passages.docid: 106884
positive_passages.text: Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?
negative_passages.docid: 143798
negative_passages.text: Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.
negative_passages.docid: 3276
negative_passages.text: Function $f:[0,1] \to [0,1]$ taking on each value in $[0,1]$ exactly twice
negative_passages.docid: 81238
negative_passages.text: Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
negative_passages.docid: 44057
negative_passages.text: Pointwise but not uniform convergence of continuous functions on $[0,1]$
negative_passages.docid: 43535
negative_passages.text: show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
negative_passages.docid: 95224
negative_passages.text: Why does triply periodic univariate function not exist?
negative_passages.docid: 11974
negative_passages.text: product of two non zero continuous function is zero
negative_passages.docid: 67644
negative_passages.text: How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
negative_passages.docid: 132013
negative_passages.text: How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
negative_passages.docid: 31244
negative_passages.text: Is this a correct bijection between $(0,1]$ and $[0,1]$?
negative_passages.docid: 90566
negative_passages.text: There exists surjections from A onto B and vice versa, and there is no bijection between the sets?
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: 134720
negative_passages.text: Show that there is no increasing function $f: \aleph_1 \to \mathbb{R}$
negative_passages.docid: 14994
negative_passages.text: Showing a function $f$ cannot be surjective
negative_passages.docid: 148638
negative_passages.text: Write $(0,1)$ as a countable union of disjoint open intervals