query: $f: Y\to X^+$ defined by $f(y)= \begin{cases} y & \text{if}\ y\in X\\ \infty & \text{else} \end{cases}$ is continuous
positive_passages.docid: 145368
positive_passages.text: How to show $f:Y\to X^{+}$ is continuous?
negative_passages.docid: 84092
negative_passages.text: If $id:(X,d_1)\to (X,d_2)$ is continuous then what will be $X$?
negative_passages.docid: 154521
negative_passages.text: Linear functional $f$ is continuous at $x_0=0$ if and only if $f$ is continuous $\forall x\in X$?
negative_passages.docid: 105652
negative_passages.text: Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
negative_passages.docid: 100187
negative_passages.text: Show function is continuous at origin
negative_passages.docid: 111290
negative_passages.text: If $f$ continuous and $\lim_{x\to-\infty }f(x)=\lim_{x\to\infty }f(x)=+\infty $ then $f$ takes its minimum.
negative_passages.docid: 143618
negative_passages.text: If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
negative_passages.docid: 154034
negative_passages.text: Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
negative_passages.docid: 48867
negative_passages.text: why all constant functions are continuous.$?$
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: 22303
negative_passages.text: How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
negative_passages.docid: 32571
negative_passages.text: Is the maximum function of a continuous function continuous?
negative_passages.docid: 44144
negative_passages.text: If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
negative_passages.docid: 23436
negative_passages.text: $f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
negative_passages.docid: 86472
negative_passages.text: $f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
negative_passages.docid: 47381
negative_passages.text: If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
negative_passages.docid: 43189
negative_passages.text: Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$