query: closure of the unit ball
positive_passages.docid: 142901
positive_passages.text: "The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
negative_passages.docid: 3649
negative_passages.text: Closed unit interval is connected proof
negative_passages.docid: 42108
negative_passages.text: Prove that $c_0$ is closed in $\ell^\infty$
negative_passages.docid: 122086
negative_passages.text: continuous function: preimage of closure of a set is closure of preimage
negative_passages.docid: 30231
negative_passages.text: The boundary of union is the union of boundaries when the sets have disjoint closures
negative_passages.docid: 40438
negative_passages.text: Proving that closed (and open) balls are convex
negative_passages.docid: 91682
negative_passages.text: Graph of a continuous function is closed
negative_passages.docid: 52629
negative_passages.text: Example 1, Sec. 22 in Munkres' TOPOLOGY, 2nd edition: How to verify that this map is closed?
negative_passages.docid: 147247
negative_passages.text: Continuous function on closed unit ball
negative_passages.docid: 103923
negative_passages.text: Double orthogonal complement is equal to topological closure
negative_passages.docid: 120685
negative_passages.text: Topology induced from Kuratowski Closure properties
negative_passages.docid: 147914
negative_passages.text: Closed image of locally compact space
negative_passages.docid: 64871
negative_passages.text: Closure of Union contains Union of Closures
negative_passages.docid: 28511
negative_passages.text: Hypervolume of a $N$-dimensional ball in $p$-norm
negative_passages.docid: 101504
negative_passages.text: An open ball is an open set
negative_passages.docid: 141642
negative_passages.text: Closure of a certain subset in a compact topological group
negative_passages.docid: 73462
negative_passages.text: Nested sequences of balls in a Banach space