Re: Cut a point into two - topological?

Bob Kolker wrote:
Hero wrote:

Regard a point as a hole , so it can be "cut" into two just as several
holes can merge into one:

How do you cut something with zero width? A point is not a set of things
so you can't split the point into two non-empty sets.


So You define a ,,cut" as a seperation of a set P into two non-empty
sets PA and PB, with P = PA union with PB, and with PA intersection
with PB = { }, and with PA =|= { } =|= PB. Did i understand You?
With it we have one defintion of a ,,cut" and that is what i'm looking
for. There must be other topological ,,cuts", as there is a cut, with
which one can open a ring.
Is for You a point a set with one element: point P = { p } ? So what
is p?
Or is for You a point P one element of a set with one element , we
have Q = { P }, so Your definition - if i did understand You - applies
to Q, not P.

With friendly greetings
Hero

.

Relevant Pages

  • Re: Cut a point into two - topological?
    ... Hero wrote: ... holes can merge into one: ... How do you cut something with zero width? ... Bob Kolker ...
    (sci.math)
  • Re: wanted: mathematician
    ... Because the way multiplication is defined, the product can't be zero unless ... "If you pick one member from each of the non-empty sets, ... infinite cardinals, ...
    (rec.arts.sf.written)
  • Re: wanted: mathematician
    ... I can try to do cliffs notes... ... Because the way multiplication is defined, the product can't be zero unless ... "If you pick one member from each of the non-empty sets, ...
    (rec.arts.sf.written)
  • Re: wanted: mathematician
    ... Cartesian product of non-empty sets is non-empty. ... cardinals, including infinite cardinals, the result is never zero. ... find the idea of multiplying an infinite number of infinities ...
    (rec.arts.sf.written)
  • Re: wanted: mathematician
    ... Cartesian product of non-empty sets is non-empty. ... cardinals, including infinite cardinals, the result is never zero. ...
    (rec.arts.sf.written)