Go ahead. Chances are that it will be very interesting to learn about.And there I was ready to build an example.
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How Many Holes Are There in a Straw?
- Thread starter SalixIncendium
- Start date
0
I'm tempted to say one hole with three openings but i may be wrong, i often am (but don't tell anyone)
Once again, 3 if you think in terms of holes in a sphere or boundaries, 2 if you do fundamental groups either internally or externally.
I'm inclined to say n=1 for an ordinary straw and n=2 for this one.
Another way to analyze it is to ask how many times you need to cut in order to get the given straw. In that case, n=2 for the usual one and n=3 here.
This is a good example of why one needs to be *very* precise about definitions. The answer you get will depend on the definition used.
RestlessSoul
Well-Known Member
Yes, one hole with three openings makes sense.
I got to zero holes through overthinking it (trying to be a smartarse); because the image is a 2 dimensional representation of a 3 dimensional object, no hole physically exists.
No - or, at least, not for any reason due to the straw.
Infinite just means "with no discernible limit". It does not mean "all-encompassing". An infinite diameter does not make such a ring a container for the whole universe.
Koch's snowflake presents a similar scenario. It has a very finite surface and exists in two dimensions with an infinitely high perimeter.
Koch snowflake - Wikipedia
en.wikipedia.org
Perhaps more relevant here is the Alexander horned sphere: Alexander horned sphere - Wikipedia
This is a 'wildly embedded' copy of a sphere with a very complicated exterior.
Yet another aspect of this is the dimensionality of holes. For example, a circle in the plane has an interior and exterior. We usually say it has one hole. But if you take a circle in 3D space, does it have a hole or not?
How about a sphere in 3D space?
It's all a matter of definitions and how we want to use the words.
A useful "2 holer"....
A non-useful "2-holer"....
A non-useful "2-holer"....
You are, of course, correct. I just don't think that topology differentiates between holes and openings, mainly because it needs a certain formal rigor to make statements.
Topology doesn't have a formal definition of either. Algebraic topology has ideas related, like the number of generators of homology or homotopy groups.