query: If real function $f$ is continuous and injective, is it strictly monotone?
positive_passages.docid: 20284
positive_passages.text: Continuous injective map is strictly monotonic
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: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 83461
negative_passages.text: Continuous iff composition with every linear functional is continuous
negative_passages.docid: 145984
negative_passages.text: if $f: (0,\infty) \to (0,\infty)$ is a strictly decreasing then $f \circ f$ is decreasing?
negative_passages.docid: 34836
negative_passages.text: Composition of Absolutely Continuous Functions
negative_passages.docid: 53738
negative_passages.text: Monotone functions and continuity
negative_passages.docid: 28315
negative_passages.text: Monotone functions and non-vanishing of derivative
negative_passages.docid: 107400
negative_passages.text: Can there be an injective function whose derivative is equivalent to its inverse function?
negative_passages.docid: 128911
negative_passages.text: Continuous extension of a real function
negative_passages.docid: 21269
negative_passages.text: Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
negative_passages.docid: 152877
negative_passages.text: Is a monotone differentiable function continuously differentiable?
negative_passages.docid: 118192
negative_passages.text: Is there a bijective function $f: \mathbb{R}\to\mathbb{R}$ that is discontinuous?
negative_passages.docid: 29154
negative_passages.text: $f$ is continuous and open implies $f$ injective
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: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 65472
negative_passages.text: From injective map to continuous map