query: Is a dense subspace of a separable topological space also separable?
positive_passages.docid: 157565
positive_passages.text: Is every dense subspace of a separable space separable?
negative_passages.docid: 67191
negative_passages.text: When is the union of a family of subspaces of a vector space also a subspace?
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 53859
negative_passages.text: Continuous image of separable space
negative_passages.docid: 8334
negative_passages.text: A reflexive Banach space is separable iff its dual is separable
negative_passages.docid: 140052
negative_passages.text: Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
negative_passages.docid: 4151
negative_passages.text: Every subspace of a vector space has a complement
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 91991
negative_passages.text: How do I prove that two closed sets are separable?
negative_passages.docid: 44430
negative_passages.text: Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
negative_passages.docid: 78082
negative_passages.text: Dense subset of two Banach spaces also dense in the intersection
negative_passages.docid: 7069
negative_passages.text: On the product of $\mathfrak c$-many separable spaces
negative_passages.docid: 109374
negative_passages.text: Is the Discrete Topology on $X$ the Only One Containing All Infinite Subsets of $X$?
negative_passages.docid: 115625
negative_passages.text: Intersection of two open dense sets is dense
negative_passages.docid: 47251
negative_passages.text: Non-compactness of $\mathbb{R}$ with the cocountable topology
negative_passages.docid: 132095
negative_passages.text: Motivation for the term "separable" in topology
negative_passages.docid: 17165
negative_passages.text: Is total boundedness a topological property?