Purchase Solution

Topological Space : Subspace

Not what you're looking for?

Ask Custom Question

Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology on Y.

Attachments
Purchase this Solution
Solution Summary

The solution to a topological space problem is explained in detail. The response received a rating of "5" from the student who posted the question.

Solution Preview

Definition of Topological Space: Suppose X is any non-empty set. Let T be a set of subsets of X such that the following are satisfied.
i) The empty set is in T i.e. and the set X is in T i.e.
ii) Arbitrary union of elements of T is an element of T i.e. where I is an index set and
iii) Finite intersection of elements of T is an element of T i.e. where , ( - the set of natural numbers) and

Then we say that ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.

Graphs and Functions

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

Multiplying Complex Numbers

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

Exponential Expressions

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

View More Free Quizzes
Related BrainMass Solutions

  • Closure of a set in a a topoogical subspace

    348254 Closure of a Set in a Topoogical Subspace 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.

  • Topological Space : Subspace

    32271 Topological Space : Subspace 19. Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology of Y.

  • Topology : Subspace

    32417 Topology : Subspace Suppose (X,T) is a topological space. Let Y be non-empty subset of X. The the set J={intersection(Y,U) : U is in T} is called the subspace toplogy on Y.

  • 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.

  • Co-Finite Topology

    Let (X,T) be a co-countable topological space. Show that X is connected if it is uncountable. In fact, show that every uncountable subspace of X is connected. 4.

  • Topology : Connected Spaces and Explosion Point

    A topological space is connected if it can not be expressed as the union of two nonempty disjoint open sets. b. Proof: Since is open in and is a subspace in , then we can find an open set in , such that .

  • Topological equivalence of an interval and the real line

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

  • Covering Spaces : Compact Hausdorff Spaces and Homomorphisms

    If s is compact subspace in a hausdorff space X , it is closed. Proof:1 Consider any point x not in s. For each y in s, embed y in an open set disjoint from an open set containing x. Do this for each y in s, and we have an open cover.

  • Three-Dimensional Topological Group

    Show that, when regarded as a subset of R4 under ( a b ) ( c d ) <--> (a, b, c, d) Exists R4 and equipped with subspace topology, SL(2) becomes a 3-dimensional topological group.

View More Related Solutions