Statement:
Existence of Complementary Subspaces over a Field \(F\): If \(F\) is a field, then every vector space \(V\) over \(F\) has the property that if \(S\subseteq V\) is a subspace of \(V\), then there is a subspace \(S'\subseteq V\) such that \(S\cap S'= \{0\}\) and \(S\cup S'\) generates \(V\). H. Rubin/J. Rubin [1985], pp 119ff, and Jech [1973b], p 148 prob 10.4.
Howard_Rubin_Number: 95-F
Parameter(s): This form depends on the following parameter(s): \(F\),
This form's transferability is: Not Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Bleicher-1964: Some theorems on vector spaces and the axiom of choice
Bleicher-1965: Multiple choice axioms and the axiom of choice for finite sets
Book references
The Axiom of Choice, Jech, T., 1973b
Equivalents of the Axiom of Choice II, Rubin, J., 1985
Note connections: