No, I read it.
It is true that in the discrete topology, the only continuous functions are constant. This is not true with the concrete topology. If X is more than one point, then f(x)=x for all x in X is a continuous, non-constant function in the concrete topology.SBRH
Since the question about concrete topology is a follow up to a question about discrete topology, I'd bet that the question was intended to have concrete replaced with discrete.
SBRH
For 1) you should use the fact that cot(x)= cos(x) / sin(x) instead of the adjacent/opposite stuff. Then try to manipulate the given equation to look like an identity that you already know.
SBRH
Topologically, a 3-sphere is the one point compactification of 3-space, so it can be thought of as 3-space with an extra point. This way of thinking completely ignores the metric unless you put a strange metric on 3-space.
A good way to visualize the geometry of the 3-sphere (or other...
Another way to do this was discovered by Archimedes, but is easy to prove using basic differential geometry.
Place the sphere inside a cylinder of radius a and height 2a so that the center of the sphere lies on the center axis of the cylinder. Define a map by projecting each point on the...