Instead of a singularity, i want to stick a klein bottle at the centre of a black hole.
Topos means place http://en.wiktionary.org/wiki/τόπος#Ancient_Greek
But place is subjectively determined by gonu-knee or rotation. semeion or mark and memory, to which may be added boundary lines or relativity bonds and bindings. Thus place is a dynamically determined notion exhibity dynamic stability not static.
If points share a line they are defined as "co" linear, but if lines share a line they are defined as identical! Big mistake. We must allow for collinear lines as well. Grassman allowed for coincident points with his notion of Schwerpunkt. Newton and Moebius used the centre of symmetry as a schwerpunkt, to which all the mass of an object was gathered or said to act. Grassmann simplified the notion by allowing a coincidence of points to reflect the amoint of ponts relative to it. In this way we may establish a notion of "punktal" or nodal relativity.
In the case of lines, if we adhere direction to them then Grassmann called them Streaks and noticed that 2 collinear streaks were the only ones that extended or decreased their attributed lengths by application of direction. All other 2 streak combinations produce a third line, which may also be taken as a streak. The same observation applies for the arcs i call twists.
If 2 straight lines lie in the same plane they are called Co planar, and again we need to extend this to planes that lie in the same plane. Then we can have coplanar magnitudes that increase or decrease their attributed areasby application of their direction. This is fundamental to the notion of "negative" magnitudes in reality.
Similarly the notion of cotopological is that the same 3d space which has planes in it defines those planes as cotopos. The planes do not have to be coplanar etc. However this allows us to extend again to 3d spaces being cotopos and then their magnitude can increase or decrease according to the application of their direction.
Clearly in all extended cases we may derive more complex applications of the general idea, but the idea itself is necessary to found the notion of "negative" magnitudes.
Clearly i am usinng the term "negative" only as shorthand here for the true directed dynamic magnitude attributes.
My favourite idea at the moment is that Shunya, the multi polar intensity field in which the fundamental motion is rotational, allows objects to move through its structure by them absorbing shunya at the front and expelling shunya at the back. Tha absorption is complex and fractal and clearly does not allow all of the field to pass through an object to be expelled at the back, some that cannot be absorbed moves round the object. The asorption and expulsion thereby allow signals to be transmitted from the moving object to the shunya field which which originate in the vorticular motions around the poles in the object, but [ropogate through the shunya field as a perceptible "wave" pattern. This wave pattern is the disturbance in the multipolar distribution as well as the rotational "symmetries" around the poles