query: Let $X=\{0,1\}$ be equipped with the indiscrete topology; Why is every $f:Y \to X$ continuous?
positive_passages.docid: 147788
positive_passages.text: Why is every map to an indiscrete space continuous?
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: 31266
negative_passages.text: Proof of "the continuous image of a connected set is connected"
negative_passages.docid: 141945
negative_passages.text: Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
negative_passages.docid: 30965
negative_passages.text: $f$ is continuous on $X$ iff $f$ is continuous on every compact subset
negative_passages.docid: 72847
negative_passages.text: Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 14578
negative_passages.text: Proving that an additive function $f$ is continuous if it is continuous at a single point
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: 14713
negative_passages.text: $X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
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: 15095
negative_passages.text: continuous onto map from $(0,1)\to (0,1]$
negative_passages.docid: 155618
negative_passages.text: Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
negative_passages.docid: 69869
negative_passages.text: if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
negative_passages.docid: 83204
negative_passages.text: Is every $G_\delta$ set the set of continuity points of some function $f$?
negative_passages.docid: 48867
negative_passages.text: why all constant functions are continuous.$?$
negative_passages.docid: 132946
negative_passages.text: Continuous and bounded imply uniform continuity?