Re: Cut a point into two - topological?

Bob Kolker wrote:

... you can't split the point into two non-empty sets.

I'm one step further on in studying geometric topologic objects, it is
spoken of holes and tunnels, but one type of objects can be
characterized so, that they can not be penetrated. The space, which is
occupied by one of these unp' objects, can not be occupied at the same
time by another. This is actually a property of material bodies, given
here also to points and lines and surfaces (all of them of volume
zero) as unp' objects. And we call the illusion, in which one of these
kind of unp' bodies pass through another apparently, magic.
So a Riemann surface, which is intersecting itself at the same time,
or a curve with a double or multiple point, is not of this unp' kind.
And the line of a circle, when described with polar coordinates, has a
range from [0, 360), just like a day has a length of 24 hours, but the
point of time of 24 hours is already 0 hours 00 minutes of the next
day.
So a point as a location can always only accomodate at the same time
one point of a material body or unpenetrateable object or being empty
or void.
Bob, did You mean this, when You wrote:
A point has no parts to seperate.
And
...you can't split the point into two non-empty sets
?
With friendly greetings
Hero


.