Topology, the worst & most wastrel subject in mathematics evidenced by Poincare conjecture and fake Perelman proof #1472 Correcting Math
When mathematics has its mathematicians precisely define infinity with a borderline between finite and infinity, such as what I found to be 1*10^603 by the tractrix and circle area, or the regular-polyhedra, then, what happens to real true math is that many subjects like Topology have nonsense questions, problems and fake proofs.
In Old Math, full of fakery, they had a continuum and so topology could prosper with fakery with a continuum. In New True Math, with a precision definition of infinity, we no longer have a continuum, but rather we have a macroinfinity border of 1*10^603 and a microinfinity border of 1*10^-603 where any smaller than 1*10^-603 is no longer mathematics. Mathematics is the subject of precision and once you go beyond finiteness, you leave mathematics.
So that in the Poincare Conjecture, there is no longer the concept of simple-connected, for each loop in geometry may shrink to a finite point, or it may shrink to a empty space of 1*10^-603, a hole or gap in the fabric of geometry.
So, much of Topology was just all phony baloney. The Poincare conjecture and the alleged Perelman proof was nothing more than fakery of mathematics.
So, the real important questions of a science of Topology, if it can exist at all, is how do we have a topology if every point has empty space on all sides of it? Here is a illustration of a square enlarged in True Math:
........ ........ ........
So, the question for Topology, if it exists, is can we shape that square to be a circle or rectangle or triangle, what were considered "Topologically Equivalent" in Old Math? Does Topology have any room in New True Math when geometry and space are alternating between a finite point and empty space between finite points.
If Topology exists at all, it is a minor subject, probably not worth being called a subject of mathematics at all. --
Recently I re-opened the old newsgroup of 1990s and there one can read my recent posts without the hassle of mockers and hatemongers.