All coverings are continuous and locally 1-1. If the covering space is compact then the covering map is also proper.
For instance, take a finite discrete set and map it onto one of its points.
1) Take a rubber band and twist it into a figure 8.
2) Take a rubber band and push two oppose points together to make a figure 8.
Keep pushing so that the rubber band intersects itself in two points.
Try the same idea with a sphere.
You are absolutely correct. I was throwing it out there partly because my anecdotal experience has seen what appears to be a shift in the interests of young people. I did look for articles and there does seem to be data that shows a decline in interest in STEM but I didn't post any links because...
For me, there was little science and I did not feel that I understood Oppenheimer's character by the end of the movie.
The contrast between the science and the war was underplayed and could have been the movie's dynamic, the frightening race to beat the Germans versus the amazing scientific...
It would be interesting to compare this professor's course with other Organic Chemistry courses in his department. On the surface it seems like he demanded less from his students than what he would have liked. So what did the other Organic Chemistry courses require? Even less? Or were the...
On the other hand, I sat in on a course elementary topology with Dennis Sullivan who was in his 70's and students and professional mathematicians alike flocked to listen to him lecture. It sounds like this Chemistry Professor was of similar caliber and probably would have inspired a genuinely...
The Painted Veil
https://www.imdb.com/title/tt0446755/
This movie is about a scientifically trained person who is dedicated to understanding and stopping a cholera epidemic. There is no stuff about his intellectual talents but just about his unflinching moral commitment, hard work, and...
That is correct.
Comments: The key theorem to know is that starting with a vector at a point on a smooth curve there is exactly one way to parallel translate it along the curve to get a vector field whose covariant derivative is zero everywhere. This is true for any affine connection. It is a...
So far the significance of the Mobius band has related to its topology, its non-orientability, its role in constructing other non-orientable surfaces, and as the simplest example of a non-trivial vector bundle. But it is also significant because it can be given a flat geometry. In this geometry...
An interesting question.
One could imagine that the Möbius band is embedded in three dimensional space and that the reflection is actually the result of a 180 degree rotation. If the Möbius band has the standard shape of a strip of paper pasted at its ends with a half twist, the flatlander will...