January 18, 2012

Does cardinality set constraints on topology? Manifolds as invariant mathematical objects? Mathematical truth?

Filed under: Letters from Ionia — Tags: , , , — zankaon @ 8:07 pm

If two separate topologically equivalent 3-manifolds are then apposed (i.e. contiguous), geometrically, or via limit, summation series, to describe degree of closeness (any continuum); then has topology changed? One could also visualize by reducing dimensions to two 1-manifolds subsequently apposed. Has the cardinality of manifolds changed, when subsequently apposed? If so, then hasn’t the topology changed? So indirectly does cardinality of manifolds set constraints on topology? In SRM, would alleged invariance of cardinality of manifolds, constrain the topology of such manifolds to be invariant for all stages? That is, 3-manifolds never intersect, nor are they ever apposed i.e. neither geometrically nor infinitesimally; and always exist? Also robust to perturbation, such as for inertia of manifold; a non-topological property?  And more generally, manifolds can neither be created nor destroyed? That is, are manifolds invariant mathematical objects, and represent mathematical truth?  see TMM


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