Purchase Solution

Real Analysis : Connected and Disconnected Sets

Not what you're looking for?

Ask Custom Question

A- Find an example of a disconnected set whose closure is connected.

b- If A is connected ,is A closure necessarily connected? If A is perfect is A closure necessarily perfect?

Purchase this Solution
Solution Summary

Connected and Disconnected Sets and Closure are investigated. The solution is detailed.

Solution Preview

a. Q is the set of rational numbers. It is obviously a disconnected set because we can find an irrational number a, such that Q is contained in the union of the two disjoint open sets (-inf,a) and (a,inf). Because Q is dense in R, so the closure of Q is R, which is connected.

b.
(1) Yes. If A is connected, the A ...

Purchase this Solution
Free BrainMass Quizzes
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.

Exponential Expressions

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

Multiplying Complex Numbers

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

Solving quadratic inequalities

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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Topology : Connected Spaces and Explosion Point

    Proof: Since , and are two nonempty disjoint open sets. Then and are disjoint. So and are disjoint. implies that . Since is disconnected, is open, then is not open.

  • Number of connected components and continuous maps, Topology

    Say we show f^{-1}(A_1) and f^{-1}(A_2) are disconnected. By assumption A_1 and A_2 are disconnected in Y, this means that there are open sets U,V subsets of Y with empty intersection and A_1 is subset of U, and A_2 is a subset of V.

  • Real analysis

    27186 Real Analysis A set E is totally disconnected if, given any two points x,y belong to E there exist separated sets A and B with x belong to A and y belong to B and E=A U B. 1-show that Q is totally disconnected. 2-is the set of irrational numbers

  • Capacitors: Energy, Voltage & Capacitance with Dielectric.

    The dielectric slab is inserted in a charged capacitor and the change in voltage and energy is calculated in two cases (1) with the battery connected and (2) battery disconnected before the slab inserted.

  • Graphs : Connectedness, Vertices and Edges

    Therefore the maximal number of edges that a disconnected graph is But G has at least , which exceeds the maximal number of edges in a disconnected graph, therefore G must be connected. (b) Let n=3, and it has edge.

  • elementary theorem in graph theory

    There are two possibilities for the given (specific) graph G: (i) It is connected (ii) It is disconnected 2. If G itself is connected, there is nothing more to prove. 3. Suppose G is disconnected.

  • disconnected data model

    User will have thier own copy data local machine and not connected to main databases.

  • Graph Theory : Connected Graphs and Disconnected Graphs

    95063 Graph Theory : Connected Graphs and Disconnected Graphs Using the theorems from Graph and Digraphs 4ed by G. Chartrand and L.

  • K-connected graph proof

    ,u_{k-1}} is connected as the new vertex can join to those vertices of v_1,v_2,...,v_k remaining in G-{u_1,...,u_{k-1}} In short, we have shown that we need to remove at least k vertices from H to make H disconnected.

View More Related Solutions