Topology of Real Unitary Space
نویسندگان
چکیده
(1) For every right zeroed non empty RLS structure V holds every Affine subset M of V is parallel to M. (2) Let V be an add-associative right zeroed right complementable non empty RLS structure and M, N be Affine subsets of V . If M is parallel to N, then N is parallel to M. (3) Let V be an Abelian add-associative right zeroed right complementable non empty RLS structure and M, L, N be Affine subsets of V . If M is parallel to L and L is parallel to N, then M is parallel to N. Let V be a non empty loop structure and let M, N be subsets of V . The functor M−N yields a subset of V and is defined by: (Def. 2) M−N = {u−v;u ranges over elements of V , v ranges over elements of V : u∈M ∧ v∈N}. One can prove the following propositions: (4) For every real linear space V and for all Affine subsets M, N of V holds M−N is Affine.
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