Purchase Solution

Topology Spaces

Not what you're looking for?

Ask Custom Question

1.
a) Suppose T_1 is a topology on X = {a,b,c} containing {a}, {b} but not {c}. Write down all the subsets of X which you know are definitely in T_1. Be careful not to name subsets which may or may not be in T_1.
b) Suppose T_2 is a topology on Y = {a,b,c,d,e} containing {a,b}, {b,c}, {c,d} and {d,e}. Write down all the subsets of X which you know are definitely in T_2. Be careful not to name subsets which may or may not be in T_2.
c) Invent a topology T_3 on Z = {a,b,c,d} containing {a}, {b,c} and {a,d}, but not {d}

2.
What is the only topology you can have on the one point set P = {x_0}? Describe it explicitly. Suppose (X, T) is a topological space. What is the only function you can have f: X-->P? Is it always sometimes or never continuous? Justify your answer.

3.
Let X be a topological space with at least two points and the indiscreet topology. Why is this not a topology that comes from a metric on X? Hint: you might like to try a proof by contradiction.

Purchase this Solution

Solution Summary

The solution provides a review on the basic topologies first, followed by a detailed solution to the problems attached.

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

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

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.