Purchase Solution

Closure of a set in a a topoogical subspace

Not what you're looking for?

Ask Custom Question

Let Y be a subspace of X and let A be a subset of Y. Denote by Cl(A_X) the closure of A in the topological space X and by Cl(A_Y) the closure of A in the topological space Y. Prove that Cl(A_Y) is a subset of Cl(A_X) . Show that in general Cl(A_Y) not equal Cl(A_X). See the attached file.

Attachments
Purchase this Solution
Solution Summary

A proof of the fact that the closure of a set in a topological subspace is a subset of the cosure of the same set in a bigger space is given. A counterexample to the equality claim is given. The solution is in a PDFfile.

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

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.

Multiplying Complex Numbers

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

View More Free Quizzes
Related BrainMass Solutions

  • Interior of a set in a topological subspace

    348256 Interior of a set in a topological subspace Let Y be a subspace of X and let A be a subset of Y. Denote by Int_X(A) the interior of A in the topological space X and by Int_Y(A) the interior of A in the topological space Y.

  • Subspace topology

    35013 Subspace Topology: Interior, Closure, Boundary and Limit Points Consider the following subsets of (FUNCTION1) and (FUNCTION2). The subspaces X and Y of (SYMBOL) inherit the subspace topology.

  • Topological equivalence of an interval and the real line

    346535 Topoogical equivalence of an open interval and the real line Prove that the open interval (-pi/2,pi/2) considered as a subspace of the real number system, topologically equivalent to the real number system.

  • Finding the interior and the closure of a set

    350871 Finding the Interior and the Closure of a Set Please see attached file. Please help write a rigorous proof on the first problem, which is called the EASY problem. Consider the set A in the attached file.

  • properties of discrete spaces

    This is just the matter of definitions. X is a discrete topoogical space if every subset of X is open. In particular, for each x in X we have {x} is an open set.

  • Weak closures

    Show that there exists an infinite dimensional subspace Y of X such that x+Y is a subset of U. Proof. The sets of the form where all are in X*, make a base for the weak neighborhoods of x .

  • Euclidean Spaces and Subspaces

    (c) Show that W is a subspace by describing W as the span of a set of vectors. (d) Explain why this subspace is a plane. Please see the attached file for the complete solution. Thanks for using BrainMass.

  • Real Analysis : Baire Category Theorem

    In particular, we will need the theorem that says a closed subspace of a compact space is compact. As before, we are given o1 o2 o3 etc, a countable collection of dense open sets. Let w be an arbitrary open set. Let x1 be a point in wà?

  • Tychonoff and Hausdorff Spaces

    b)Any open subset U of a compactly generated space X is compactly generated if each point has an open neighborhood in X with closure contained in U. c)Show that a space is Tychonoff iff it can be embedded in a cube.

View More Related Solutions