Recent content by jimisrv

Hi, I am having some problems understanding the degree of a continuous map g:circle --> circle I have found a definition in Munkres (pg 367) that I can't really understand (I'm an engineering student with little algebraic topology) and one in Lawson (pg 181), Topology:A Geometric approach...

Hi, Easy question about connectedness. I have from Munkres that the finite Cartesian product of connected sets is connected. How about for simply connected sets? This seems like a natural extension of the theorem. Would you say I need to offer a proof? Simply connectedness seems to require...

Hi, I have a conceptual question. In a project I am working on, we are dealing with \Re^{n} (with the usual topology), and I am working on characterizing some objects. In particular, I am dealing with the intersection of two simply connected open sets (that do not have any sort of...

Thanks for the help! The last one is a very simple counterexample.

Hi, I have a question that I'm not sure about. If f:A->C is continuous and B is a subset of C that is simply connected, is f(^-1)(B) necessarily connected or simply connected for that matter? Since the spaces are not necessarily homeomorphic I cannot consider it a topological invariant...

Hi, I have a quick question: When we talk about smooth functions (say a vector field on Rn), why must we usually restrict the domain to an open set in Rn? Thanks!

I would assume that all physical science/engineering majors are at least exposed to linear algebra in an applied context (in the sense of solving linear equations, determinants, Eigen value problems, linear vector ODE's etc.). Physics, math, EE, Econ, ME all generally offer more advanced upper...