query: Showing that projection map on Cartesian products is surjective requires axiom of choice?
positive_passages.docid: 153634
positive_passages.text: A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
negative_passages.docid: 113109
negative_passages.text: Showing that a map is bijective and finding its inverse
negative_passages.docid: 116732
negative_passages.text: Proving that a continuous map is surjective
negative_passages.docid: 150385
negative_passages.text: The use of the Axiom of Choice in this proof of the sequence lemma
negative_passages.docid: 102383
negative_passages.text: Associativity of Cartesian Product
negative_passages.docid: 29755
negative_passages.text: Power set equivalency of Axiom of Choice
negative_passages.docid: 19414
negative_passages.text: Uncountable subset with uncountable complement, without the Axiom of Choice
negative_passages.docid: 115272
negative_passages.text: Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 6023
negative_passages.text: Surjectivity of Composition of Surjective Functions
negative_passages.docid: 32774
negative_passages.text: Finite Cartesian Product of Countable sets is countable?
negative_passages.docid: 9651
negative_passages.text: Cardinality of cartesian product of an infinite set with N
negative_passages.docid: 65888
negative_passages.text: A counterexample to theorem about orthogonal projection
negative_passages.docid: 88051
negative_passages.text: $\mathbb R = X^2$ as a Cartesian product
negative_passages.docid: 128266
negative_passages.text: Dual Spaces and Natural maps
negative_passages.docid: 19245
negative_passages.text: Schwartz Distribution Theory: (Non-)Surjectivity of $f \mapsto f*f$ in $ \mathcal E '$
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice