**
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 may overlap.

**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 21^{st} century Theory of Everything in any domain.
It unifies many knowledge fields.

** Applications.**

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]*

Books:

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

Articles:

**Neutrosophic Transdisciplinarity (Multispace and Multistructure)****Smarandache Multi-Space Theory (I) - Algebraic multi-spaces, by Linfan Mao, 2006, http://xxx.lanl.gov/pdf/math/0604480v1****Smarandache Multi-Space Theory (II) - Multi-spaces on graphs, by Linfan Mao, 2006, http://xxx.lanl.gov/pdf/math/0604481v1****Smarandache Multi-Space Theory (III) - Map geometries and pseudo-plane geometries, by Linfan Mao, 2006, http://xxx.lanl.gov/pdf/math/0604482v1****Smarandache Multi-Space Theory (IV) - Application to theoretical physics, by Linfan Mao, 2006, http://xxx.lanl.gov/pdf/math/0604483v1**- A multi-space model for Chinese bids evaluation with analyzing, by Linfan Mao, 2006, http://xxx.lanl.gov/pdf/math/0605495v1
- A Generalization of Seifert-Van Kampen Theorem for Fundamental Groups, by Linfan Mao, 2010, http://xxx.lanl.gov/pdf/1006.4071v1
- On Algebraic Multi-Ring Spaces, by Linfan Mao, 2005, http://xxx.lanl.gov/pdf/math/0510478v1
- On Multi-Vector Spaces, by Linfan Mao, 2005, http://xxx.lanl.gov/pdf/math/0510479v1
**On Multi-Metric Spaces, by Linfan Mao, 2005, http://xxx.lanl.gov/pdf/math/0510480**

*
First International Conference on Smarandache Multispace and Multistructure*

was organized by Dr. Linfan Mao [maolinfan@163.com], 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: **

**
http://www.ams.org/meetings/calendar/2013_jun28-30_beijing100190.html
**

**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.

** **