query: Let $c_1,c_2:X\to Y$ be continuous functions. Show that the set $P=\{x\in X\mid c_1(x)=c_2(x)\}$ is closed in $X$
positive_passages.docid: 16735
positive_passages.text: If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
negative_passages.docid: 86317
negative_passages.text: Show that $F\subset Y$ is closed in $Y$ iff $F=Y\;\cap\;H$ where $H\subset X$ is closed in $X$.
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 3649
negative_passages.text: Closed unit interval is connected proof
negative_passages.docid: 14516
negative_passages.text: The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
negative_passages.docid: 42494
negative_passages.text: The boundary is a closed set
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 151410
negative_passages.text: Inequality of continuous functions
negative_passages.docid: 99236
negative_passages.text: Interior of closure of an open set
negative_passages.docid: 100740
negative_passages.text: proof of that a continuous function has a fixed point
negative_passages.docid: 76689
negative_passages.text: How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
negative_passages.docid: 143105
negative_passages.text: Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
negative_passages.docid: 106718
negative_passages.text: Prove if C is midpoint convex and closed then its a convex set
negative_passages.docid: 10180
negative_passages.text: How to prove that this set is closed?
negative_passages.docid: 157603
negative_passages.text: Continuity $\iff$ Preimage is closed whenever set is closed
negative_passages.docid: 97316
negative_passages.text: Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X
negative_passages.docid: 125682
negative_passages.text: Proof verification: the product of two continuous functions is continuous