Multispace & Multistructure

    In any domain of knowledge, a Smarandache multispace (or S-multispace) with its multistructure is a finite or infinite (countable or uncountable) union of many spaces that have various structures. The spaces and the structures may be non-disjoint.

The notions of multispace (also spelt multi-space) and multistructure (also spelt multi-structure) were introduced by Smarandache in 1969 under his idea of hybrid science: combining different fields into a unifying field, which is closer to our real life world since we live in a heterogeneous space.

Today, this idea is widely accepted by the world of sciences.

S-multispace is a qualitative notion, since it is too large and includes both metric and non-metric spaces. 


It is believed that the smarandache multispace with its multistructure is the best candidate for 21st century Theory of Everything in any domain. It unifies many knowledge fields.


A such multispace can be used for example in physics for the Unified Field Theory that tries to unite the gravitational, electromagnetic, weak and strong interactions.

Or in the parallel quantum computing and in the mu-bit theory, in multi-entangled states or

particles and up to multi-entangles objects.


We also mention: the algebraic multispaces (multi-groups, multi-rings, multi-vector spaces, multi-operation systems and multi-manifolds, also multi-voltage graphs, multi-embedding of a graph in an n-manifold, etc.), geometric multispaces (combinations of Euclidean and Non-Euclidean geometries into one space as in Smarandache geometries), theoretical physics, including the relativity theory, the M-theory and the cosmology, then multi-space models for p-branes and cosmology, etc.

- The multispace and multistructure were first used in the Smarandache geometries (1969), which are combinations of different geometric spaces such that at least one geometric axiom behaves differently in each such space.

- In paradoxism (1980), which is a vanguard in literature, arts, and science, based on finding common things to opposite ideas [i.e. combination of contradictory fields].

- In neutrosophy (1995), which is a generalization of dialectics in philosophy, and takes into consideration not only an entity <A> and its opposite <antiA> as dialectics does, but also the neutralities <neutA> in between. Neutrosophy combines all these three <A>, <antiA>, and <neutA> together. Neutrosophy is a metaphilosophy.

- Then in neutrosophic logic (1995), neutrosophic set (1995), and neutrosophic probability (1995), which have, behind the classical values of truth and falsehood, a third component called indeterminacy (or neutrality, which is neither true nor false, or is both true and false simultaneously - again a combination of opposites: true and false in indeterminacy).

-  Also used in Smarandache algebraic structures (1998), where some algebraic structures are included in other algebraic structures.

[Dr. Linfan Mao, Chinese Academy of Sciences, Beijing, P. R. China]


bullet Smarandache Multi-Space Theory (partially post-doctoral research for the Chinese Academy of Sciences), by Linfan Mao
bullet Combinatorial Geometry with Applications to Field Theory (second edition), graduate textbook in mathematics, by L. Mao
bullet Proceedings of the First International Conference on Smarandache Multispace & Multistructure


bullet Neutrosophic Transdisciplinarity (Multispace and Multistructure)
bullet Smarandache Multi-Space Theory (I) - Algebraic multi-spaces, by Linfan Mao, 2006, 
bullet Smarandache Multi-Space Theory (II) - Multi-spaces on graphs, by Linfan Mao, 2006,
bullet Smarandache Multi-Space Theory (III) - Map geometries and pseudo-plane geometries, by Linfan Mao, 2006,
bullet Smarandache Multi-Space Theory (IV) - Application to theoretical physics, by Linfan Mao, 2006,
bullet A multi-space model for Chinese bids evaluation with analyzing, by Linfan Mao, 2006,
bullet A Generalization of Seifert-Van Kampen Theorem for Fundamental Groups, by Linfan Mao, 2010,
bullet On Algebraic Multi-Ring Spaces, by Linfan Mao, 2005,
bullet On Multi-Vector Spaces, by Linfan Mao, 2005,
bullet On Multi-Metric Spaces, by Linfan Mao, 2005,

First International Conference on Smarandache Multispace and Multistructure

was organized by Dr. Linfan Mao [], Academy of Mathematics and Systems, Chinese Academy of Sciences, Beijing 100190, People's Republic of China, between June 28-30, 2013.

See the American Mathematical Society’s Calendar website:

In recent decades, Smarandache’s notions of multispace and multistructure were widely spread and have shown much importance in sciences around the world. Organized by Prof. Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.

 The Smarandache multispace and multistructure are qualitative notions, but both can be applied to metric and non-metric systems. There were 46 researchers haven taken part in this conference with 14 papers on Smarandache multispaces and geometry, birings, neutrosophy, neutrosophic groups, regular maps and topological graphs with applications to non-solvable equation systems.


Prof. Yanpei Liu reports on topological graphs


Prof. Linfan Mao reports on non-solvable systems of equations

Prof. Shaofei Du reports on regular maps with developments

   Applications of Smarandache multispaces and multistructures underline a combinatorial mathematical structure and interchangeability with other sciences, including gravitational fields, weak and strong interactions, traffic network, etc.

All participants have showed a genuine interest on topics discussed in this conference and would like to carry these notions forward in their scientific works.


MATHEMATICS Algebra Geometries Multispace
  Neutrosophic Environment Number Theory Statistics
  Plithogenic Set / Logic /      Probability / Statistics    
PHILOSOPHY Neutrosophy, a new branch of philosophy Law of Included Multiple-Middle & Principle of Dynamic Neutrosophic Opposition  
PHYSICS Absolute Theory of Relativity Quantum Paradoxes Unmatter
  Neutrosophic Physics Superluminal and Instantaneous Physics  
BIOLOGY Neutrosophic Theory of Evolution Syndrome  
ECONOMICS Poly-Emporium Theory    
LINGUISTICS Linguistic Paradoxes Linguistic Tautologies  
PSYCHOLOGY Neutropsychic Personality Illusion Law on Sensations and Stimuli
  Synonymity Test Complex  
SOCIOLOGY Social Paradox Sociological Theory  
  Literatura Romana Bancuri Travel Memories
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