query: No bijective continuous $f:(0,1) \to [0,1]$ using facts from topology?
positive_passages.docid: 38257
positive_passages.text: Continuous bijection from $(0,1)$ to $[0,1]$
negative_passages.docid: 33330
negative_passages.text: Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
negative_passages.docid: 72642
negative_passages.text: Continuous bijection from $(a,b) \to S^1$?
negative_passages.docid: 40209
negative_passages.text: $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
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: 62793
negative_passages.text: $\mathbb{R}$ with the lower limit topology is not second-countable
negative_passages.docid: 22210
negative_passages.text: Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
negative_passages.docid: 100465
negative_passages.text: Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
negative_passages.docid: 94899
negative_passages.text: Graph of a continuous function has measure zero
negative_passages.docid: 134575
negative_passages.text: Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
negative_passages.docid: 92089
negative_passages.text: If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
negative_passages.docid: 1117
negative_passages.text: Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
negative_passages.docid: 68165
negative_passages.text: Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 72115
negative_passages.text: Why isn't there a continuously differentiable surjection from $I \to I \times I$?
negative_passages.docid: 158842
negative_passages.text: What is wrong with this bijection from all naturals to reals between 0 and 1?