The question I had was to show that if a function is continuous, open and bijective then it is a homeomorphism. At first I said "no" because I thought of the example showing that [0,2pi) is not homeomorphic to the unit circle S. I knew that f(x)=(sinx,cosx) is a continuous bijection whose...
Homework Statement
show the sequence sn= (n+1)1/2 - n1/2 converges to zero
Homework Equations
The Attempt at a Solution
I don't have that much of a problem showing the limit goes to zero, rationalize the numerator (or whatever it's called) to get (n+1)1/2 - n1/2 = 1/((n+1)1/2 +...
Abstract Algebra- VERY SIMPLE but I don't understand what my HW question is asking!
Homework Statement
Hi. I am having trouble simply understanding what the question is here:
(6) let w = (1 2 3 4 5 6 7 8 9 10 11 12 13 14). For which integers i is w^i a 14-cycle?
Here is a link...
I don't know if this is more appropriate for the topology forum, but I am learning this in analysis. I am asked to say whether or not Q and N are homeomorphic to each other and to justify why. I am confused as to how to prove precisely that two spaces are homeomorphic, for there are no formal...