A Smarandache multi-space is a union of n diversified areas equipped
with assorted constructions for an integer n ≥ 2, which are used for structures either in
nature or humans. This textbook introduces Smarandache multi-spaces such as
those of algebraic multi-spaces, together with graph multi-spaces, multi-groups, multi-rings,
multi-fields, vector multi-spaces, geometrical multi-spaces, relatively map geometry
with or with no boundary, pseudo-Euclidean geometry on Rn, combinatorial Euclidean
spaces, combinatorial manifolds, topological teams and topological multi-groups, combinatorial
metric areas, • • •, and so on. and purposes of Smarandache multi-spaces, particularly
to physics, economic climate and epidemiology. in reality, Smarandache multi-spaces
underlying graphs are a tremendous systematically thought for clinical examine in 21st
century. This publication should be acceptable for graduate scholars in combinatorics, topological
graphs, Smarandache geometry, physics and macro-economy as a textbook.

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