Usually, one holds a thing T on its appearance or characters and particularly, by mathematics. But is the mathematical reality equal to the reality of thing T? The answer is not certain because the recognition of human on thing T is only a local or conditional one, implied in the fable of blind men with an elephant, i.e., the sophist told the blind men that an elephant has all characteristics that they are talking about. Then, what is the significance of this fable? It lies essentially in the shape of an elephant and generally, the reality of a thing is a combinatorial one, i.e., combinatorics is priori to the recognition of human because all of us are similar to the blind in front of a thing. In this report, I discuss the non-harmonious group with Smarandache multispace inherited a topological graph G in first, generalize it to G-flows or networks with vector flows and then, continuity flows , i.e., mathematics over 1-dimensional topological graphs, which extends the classic mathematics over combinatorial structures . This report surveys how to establish such a system by viewing continuity flow as a mathematical element for establishing the Banach flow space, Hilbert flow space over topological graphs and then, how to apply it to generalize a few of important conclusions in functional analysis such as those of the inverse mapping theorem, closed graph theorem and the Hahn-Banach theorem for providing the recognition of human on the reality of things, including the subdivision of a matter M into elementary particles with a mathematical supporting, which forms a complex network on M in physics, and shows also the 12 meridians on human body in traditional Chinese medicine is an example of G-flows or generally, continuity flows.
Key Words: Combinatorial notion, contradiction, non-solvable system of equations, nonharmonious group, Smarandachely denied axiom, Smarandache multispace, G-flow, continuity flow, mathematical combinatorics, 12 meridians on human body.
AMS(2010): 05C10, 05C21, 35A08, 46B25, 51D20, 51H20, 51P05.

Dr. Linfan Mao is a researcher of Chinese Academy of Mathematics and System Science, the president and chief-scientist of Academy of Mathematical Combinatorics & Applications (AMCA, USA), the dean of Yuan-Ling Data Academy of Complex System, an adjunct professor of Beijing University of Civil Engineering and Architecture, Honorary Fellow of the International Association of Neutrosophic Science(NAIS, USA) and the editor-in-chief of International Journal of Mathematical Combinatorics (ISSN 1937-1055, founded in 2007). He got his Ph.D in Northern Jiaotong University in 2002 and finished his postdoctoral report for Chinese Academy of Sciences in 2005. His mainly research interest includes the mathematical combinatorics and Smarandache multispaces with applications to sciences, includes combinatorics, algebra, topology, differential geometry, theoretical physics and parallel universe, having published over 120 academic papers in academic journals, and published 8 mathematical books and several collections of academic papers. His most famous books and papers include Combinatorial Geometry with Application to Field Theory, Combinatorial Theory on the Universe, Combinatorial Speculation and Combinatorial Conjecture for Mathematics, and Mathematics on Non-Mathematics -- A Combinatorial Contribution. He won the Albert Nelson Marquis Lifetime Achievement Award, endorsed by Marquis Who's Who as a leader in the fields of mathematics and engineering in 2017.