Explore BrainMass

# General and Differential Topology

Not what you're looking for? Search our solutions OR ask your own Custom question.

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

Find conditions under which the box topology is strictly finer than the product topology. See attached file for full problem description.

https://brainmass.com/math/geometry-and-topology/general-differential-topology-49380

#### Solution Preview

Question:

Find conditions under which the box topology is strictly finer than the product topology.

Definition of Box Topology:

Let I be an arbitrary index set and suppose X_i is a topological space for every i in I. Set X = &#928; X_i, the cartesian product of the sets X_i.
The box topology is generated by the collection B = { &#928; U_i | U_i open in X_i}, the cartesian products of every open set of every X_i.

Definition ...

#### Solution Summary

The general and differential topology is examined. The conditions under which the box topology is strictly finer than the product topology is provided.

\$2.49