Mathematically, topological vector space has been the key to encompass the study of energy and matter in terms of continuum mechanics and boundedness. However, in order to include time aspects, especially with respect to velocity as well as acceleration, it may be necessary to expand the notion to topological vector space time, taking expanding nature of universe into account. In other other words, a dynamic universe may need the consideration of topological vector space time. Mathematically, this will help in operating on the general theory to grand theory.
Hello George,
Thank you with your information. ".....The latter seems to be a physical issue, not mathematical...". Will that mean we can change definition to take care of that?
Sincerely,
Rajan Iyer
Hello George,
Thank you with your clarification. Please inform whether there is a way to do that without affecting logical mathematical flow of theory, helping generalization of concept.
Sincerely,
Rajan Iyer
YES--BECAUSE...TOPOLOGICAL PRESSURE IS CREATED BY DISCONTINUOUS VECTOR POTENTIALS which have saddle points with "large" Lyapunov exponents creating topological vector space time ("liquid time")...three-dimensional vortex structures for moderate Reynolds numbers...a FOMENKO SKELETON.
Hello Susana,
Thank you with your information. The next question is whether subsets of topological vector space time, velocity and acceleration form Abelian Lie Groups.
Sincerely,
Rajan Iyer
Only abelian Lie groups have connections with no curvature and no torsion. Having no torsion they can be stated as metric connections
FOR EXAMPLE-The smooth manifold P³ can be assigned different connections. One possibility is an isotropic constant-curvature torsion-free connection. This is a metric connection and makes P³ look locally as a 3-sphere. Another possibility is an isotropic no-curvature connection with torsion. This is the one that makes P³ into a Lie group. Since the connection has torsion it cannot be stated as a metric. The torsion manifests itself as non-commutativity of the Lie group.THIS IS WHERE A4 PROJECTION CAN HELP BUT ONLY IN 2-D-The notion of topological space aims to axiomatize the idea of a space as a collection of points that hang together (“cohere”) in a continuous way.(THIS IS KEY TO CYBERNETICS AND TRANSHUMAN TECHNOLOGIES)-The Morse Function gives you genus and the orientability...iN MY OPINION WE NEED REDEFINITION OF ENERGY AS A VECTOR AND CONSEQUENTLY MASS...IT'S ALL ABOUT PRESSURE!
Hello Susana,
Thank you with your insight. Yes, because velocity and acceleration are primary parameters of equation of motion, I am trying to have metrically transitioning to energy and field to express conjugate self similar subsets of topological vector space time +/-. I am hoping having publications with you on mathematics and physics that will eventually form fundamental approach to a grand unified theory of everything.
Sincerely,
Rajan Iyer
THANK YOU RAJAN...I'D LIKE THAT TOO....IT IS VERY EXCITING TO BE RIGHT AT THE EDGE...! :-)....WE CAN TALK ABOUT YOUR IDEAS...SEND ME AN EMAIL
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