Purchase Solution

General and Differential Topology

Not what you're looking for?

Ask Custom Question

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

Attachments
Purchase this Solution

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.

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 = Π X_i, the cartesian product of the sets X_i.
The box topology is generated by the collection B = { Π U_i | U_i open in X_i}, the cartesian products of every open set of every X_i.

Definition ...

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

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.

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.