Part Four of Session Seven of Course 19 -- The Klein Bottle and Orbifold Differentiaion

A supremumization is when one integrates a physical space into three extra spatial dimensions.  So, if one were to take a supremumization of a supremumization of an initial six spatial dimension-based Minkowski Space -- one will then have a twelve dimensional-based Minkowski Space.  Such a just eluded-to twelve-dimensional Minkowski surface or flat-based surface may often be considered as a volume-based space or a Hilbert Space,  instead.  (A Minkowski Space is a flat-based space, and, a Hilbert Space is a volume-based space.)  So, if one were to be initially considering a ten-dimensional Hilbert Space -- that is subsequently double-integrated into two additional spatial dimensions, into what will then be a twelve-dimensional Hilbert Space -- then, what this will here amount to, is the generally taken Laplacian-based condition of having the extrapolation of a majorization of a ten-dimensional volume-based space into a twelve-dimensional volume-based space.  One can have a flat space that may have up to 26 spatial dimensions, plus time.  The condition as to whether or not one is dealing with the consideration of either a flat-space or a Minkowski-based space or a volume-space or a Hilbert-based space, is whether or not one is either to be able to or to not be able to treat the space-time-based fabric in which one is to go through, over time, as a contortable sheet that is not viably travelled through in a transversel-based manner otherwise, or, instead, if one is to treat the space-time-based fabric in which one is to go through, as actually being a viably travelled through operand -- that would here be traveled through in a transversel-based manner, respectively.  A volume-based space or a Minkowski Space is most associated with a worm-hole that would -- in this case -- bear all of its additive source of velocity to the condition of the bending of space-time-fabric.  Yet, if any of the additive source of the velocity at all that is caused by the activity  of traveling through a given arbitrary worm-hole is due to a respective given arbitrary tense of a tachyonic propulsion, then, the manner of describing the nature of the space that would here be traveled through, would be a twelve-dimensional volume-based space or a twelve-dimensional Hilbert space -- when this is not including the dimensionality due to time itself.