query: X contains all its accumulation points $\iff$ X contains all its closure points.
positive_passages.docid: 156594
positive_passages.text: boundary points, isolation points, accumulation points.
negative_passages.docid: 152193
negative_passages.text: The intersection of a closure with an open set
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: 42150
negative_passages.text: Prove that $\forall x \neg P(x) \iff \neg \exists x P(x)$
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: 67541
negative_passages.text: When does "X is NP-complete" imply "#X is #P-complete"?
negative_passages.docid: 47680
negative_passages.text: Prove that the union of the interior of a set and the boundary of the set is the closure of the set
negative_passages.docid: 32910
negative_passages.text: Completion and algebraic closure commutable
negative_passages.docid: 74312
negative_passages.text: If Y is complete then B(X,Y) is complete
negative_passages.docid: 5448
negative_passages.text: Finding the closure of some subsets of the ordered square
negative_passages.docid: 123753
negative_passages.text: In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
negative_passages.docid: 73338
negative_passages.text: Prove that the closure of complement, is the complement of the interior
negative_passages.docid: 12490
negative_passages.text: A map is continuous if and only if for every set, the image of closure is contained in the closure of image
negative_passages.docid: 21176
negative_passages.text: Closure of the set in dictionary order topology.
negative_passages.docid: 102048
negative_passages.text: Closure of a compact set in Regular space $ X $
negative_passages.docid: 150011
negative_passages.text: Proof completeness of $(X,d)$ given $d$ is French railway metric
negative_passages.docid: 50344
negative_passages.text: What is the closure of an open ball $B_X(\mathbf{a},r)$ in $X=\mathbb{R}^n$?