Purchase Solution

Topological equivalence of an interval and the real line

Not what you're looking for?

Ask Custom Question

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.
Prove that any two open intervals, considered as subspaces of the real number system, are topologically equivalent.
Prove that any open interval, considered as a subspace of the real number system, is topologically equivalent to the real number system.

Attachments
Purchase this Solution
Solution Summary

The proof of the topological equivalence of an interval in the real line and the real line itself is given

Solution Preview

Two topological spaces X and Y are topologically equivalent if thereis a homeomorphism between them, that is, a continuous bijective map f: X -> ...

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.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

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

View More Free Quizzes
Related BrainMass Solutions

  • Having the same homotopy type equivalence

    74071 Having the same homotopy type equivalence Prove that "having the same homotopy type" is an equivalence relation on the set of topological spaces.

  • Homotopic proof

    Show that 'homotopic relative A' defines an equivalence relation on the set of continuous maps from X to Y which agree with some fixed map on A. --- Please see the attached file. This is a proof regarding a homotopy and equivalence relation.

  • Real Analysis : Topological Characterization of Continuity

    29763 Real Analysis: Topological Characterization of Continuity Let g be defined on all of R.if A is a subset of R define the set g^-1 (A) by g^-1 (A)={x belong to R:g(x) belong to A}.

  • Contractible spaces

    If f is a continuous, then we define f as follows: f: [a,b]  X for some closed interval in the real line into X such that f(a) = x and f(b) = y. Thus X is path connected if every pair of points (x,y) in X can be joined by a path f in X.

  • Equivalence Relation on the set R of all Real Numbers

    (b) B={x: x is an element of R and 0 <= x < 1} (c) for real numbers x and y, "x==y" (x is equivalent to y) if and only if x - y is an element of Z (the set of all integers) (d) "A==" denotes the set of all equivalence classes The following are the

  • Real Analysis

    243812 Real Analysis: Topological Spaces In the textbook: Topological spaces 1.Compactness in Metric spaces (Sections 11.1-11.4) Problems: - Section 11 --# 1,2,3,4 2.Real functions on Metric and Topological Spaces (Sections 12.1.12.2

  • Topological Spaces and Continuity

    164576 Topological Spaces and Continuity Please see the attached file for the fully formatted problems. Let be a real valued function on a topological space .

  • Equivalence Relations

    11366 Equivalence Relations and Class Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically. 1) (x1,y1)R(x2,y2) if and only if x1 = x2 2) (x1,y1

  • Linear Mapping in Subsets

    Question 2 Let (0,1) denote the open unit interval in R, and C(0,1) the set of all continuous functions (0,1) ---> R. Is C(0,1) a subset of B((0,1),R) the set of all bounded functions on (0,1)?

View More Related Solutions