zankaon

March 20, 2017

Can manifolds change; or are they invariant?

Filed under: Letters from Ionia — Tags: , — zankaon @ 5:12 pm

No manifold concept can, in a simplified sense, be refered to as just a surface. Thus shape is irrelevant; hence change in shape is not pertinent.

Manifold can be rendered as contiiii8nuum; that is an inbetweeness quality, wherein one has a mapping of nearby elements of respective sets. Can one even have a minimum number (3) of elements required to define closeness and inbetweeness?


So can a manifold change; that is change it’s continuum? Or add additional inclusiv.e new continua vis a product space construction, giving successively a new higher dimensional space?


Would bifurcation and merging of manifolds be impossible, even of same continua? Exemplified by no merging of hot Jupiters’ with respective star, even over billion of years? Thus also consistent with no coalescence of compact objects? Also would above be compatable with no bifurcating of manifolds, as in eternal chaotic inflation, nor with merging of 3-branes, nor of patches of different manifold arising within a given manifold, nor of non-manifold suddenly appearing i.e. singularity etc.?


Thus are manifolds stable? Thus no creation nor destruction of manifolds. Hence for example, consistent with a divergent set of entangled always disjoint manifolds?


Would all of this seem consistent with concept of manifolds being truculent, and difficult to deal with? As if  they want to be left alone; perhaps because they are not capable of change i.e. always invariant? 

Modified Set Model at HTTP://sites.Google.com/site/zankaon

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