Explore BrainMass
Share

Let X=X1 x X2 x...x Xn be the product space of the path connected topological space X1, X2, ..., Xn. Prove that the product space X is also path connected.

This content was STOLEN from BrainMass.com - View the original, and get the solution, here!

Let X=X1 x X2 x...x Xn be the product space of the path connected topological space X1, X2, ..., Xn.
Prove that the product space X is also path connected.

Please see the attached file for the fully formatted problems.

© BrainMass Inc. brainmass.com September 24, 2018, 1:34 am ad1c9bdddf - https://brainmass.com/math/geometry-and-topology/product-space-path-connected-topological-space-56546

Attachments

Solution Summary

Path-connectedness is proven. The solution is detailed and well presented. The product space of the path connected topological spaces are determined.

$2.19