Definition. Let (X,F) be a topological space. For Y c X, the collection Ty = {U|U = VoY for some V E I} %3D is a topology on Y called the subspace topology. It is also called the relative topology on Y inherited from X. The space (Y, Fy) is called a (topological) subspace of X. If U E Ty we say U is open in Y. Theorem 3.25. Let (X,J) be a topological space and Y c X. Then the collection of sets Ty is in fact a topology on Y.

Definition. Let (X,F) be a topological space. For Y c X, the collection Ty = {U|U = VoY for some V E I} %3D is a topology on Y called the subspace topology. It is also called the relative topology on Y inherited from X. The space (Y, Fy) is called a (topological) subspace of X. If U E Ty we say U is open in Y. Theorem 3.25. Let (X,J) be a topological space and Y c X. Then the collection of sets Ty is in fact a topology on Y.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...

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Could you show me how to do 3.25 in detail?

Definition. Let (X,J) be a topological space. For Y c X, the collection
Fy = {U |U = VnY for some VE I}
is a topology on Y called the subspace topology. It is also called the relative topology
on Y inherited from X. The space (Y, Ty) is called a (topological) subspace of X. If
U E Ty we say U is open in Y.
Theorem 3.25. Let (X,J) be a topological space and Y c X. Then the collection of sets
Ty is in fact a topology on Y.

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