Purchase Solution

Covering Spaces : Compact Hausdorff Spaces and Homomorphisms

Not what you're looking for?

Ask Custom Question

Assume X and Y are arcwise connected and locally arcwise connected, X is compact Hausdorff, and Y is Hausdorff. Let f: X-->Y be a local homeomorphism. Prove that (X,f) is a covering space.

Purchase this Solution

Solution Summary

Covering Spaces, Compact Hausdorff Spaces and Homomorphisms are investigated. The solution is detailed and well presented.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Covering Spaces: Algebraic Topology problem
________________________________________
Assume X and Y are arcwise connected and locally arcwise connected,
X is compact Hausdorff, and Y is Hausdorff. Let f: X-->Y be a local homeomorphism. Prove that (X,f) is a covering space.

Solution:

an arc connecting two points and of a topological space is not simply (like a path) a continuous function such that and , but must also have a continuous inverse function, i.e., that it is a homeomorphism between and the image of f.

If s is compact subspace in a ...

Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts