query: Show that no $T\in \mathcal{K}(X,Y)$ is onto.
positive_passages.docid: 44738
positive_passages.text: Compact operators on an infinite dimensional Banach space cannot be surjective
negative_passages.docid: 132382
negative_passages.text: Showing a set is nowhere dense in $C([0,1])$
negative_passages.docid: 152057
negative_passages.text: Let $(X,d)$ be a compact metric space. Let $f: X \to X$ be such that $d(f(x),f(y)) = d(x,y)$ for all $x,y \in X$. Show that $f $ is onto (surjective).
negative_passages.docid: 93771
negative_passages.text: Prove that for any set $A$ there is some $x \notin A$
negative_passages.docid: 122536
negative_passages.text: Show that any finite $T_1$-space $X$ is discrete.
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 52014
negative_passages.text: Showing $(C[0,1], d_1)$ is not a complete metric space
negative_passages.docid: 155999
negative_passages.text: How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
negative_passages.docid: 4518
negative_passages.text: How would one go about proving that the rationals are not the countable intersection of open sets?
negative_passages.docid: 100121
negative_passages.text: Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 151553
negative_passages.text: Big-O proof showing that t(n) is O(1)
negative_passages.docid: 111129
negative_passages.text: Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
negative_passages.docid: 12402
negative_passages.text: Showing a function on $[0,1]$ is the zero function
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.