query: Non-principal ultrafilters on a set
positive_passages.docid: 27058
positive_passages.text: Construction of Ultrafilters
negative_passages.docid: 51313
negative_passages.text: Extension of linearly independent set to a basis in an infinite dimensional vector space
negative_passages.docid: 116378
negative_passages.text: Nonhomeomorphic subsets of the plane
negative_passages.docid: 4213
negative_passages.text: The set that only contains itself
negative_passages.docid: 95074
negative_passages.text: Separability of $l^{p}$ spaces
negative_passages.docid: 42095
negative_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 272
negative_passages.text: Cantor Sets/nonempty/cardinality
negative_passages.docid: 84394
negative_passages.text: Choice function for a collection of nonempty subsets of $\{0,1\}^\omega$
negative_passages.docid: 9330
negative_passages.text: Meaning behind Filter in Set Theory
negative_passages.docid: 117533
negative_passages.text: $|A-\lambda I|$ and $|\lambda I-A|$
negative_passages.docid: 110832
negative_passages.text: $F_\sigma$-subsets in a normal space can be separated
negative_passages.docid: 97557
negative_passages.text: supremum of uncountable families of Borel measurable functions
negative_passages.docid: 85915
negative_passages.text: Principal prime ideals are minimal among prime ideals in a UFD
negative_passages.docid: 88099
negative_passages.text: Not $\sigma$-compact set without axiom of choice
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 24050
negative_passages.text: Characterization of the Closure of a Set
negative_passages.docid: 146664
negative_passages.text: The union of two linearly independent subsets