I think I am on the right track but I might be wrong. The work provided is what I have done. Let $ (X, \mathcal{T}) $ be a topological space and suppose that $ A $ and $ B $ are subsets of $ X $ such that $ A \subseteq B $. Prove that $ A^\circ \subseteq B^\circ $ and $ \overline{A} \subseteq \overline{B} $. **Proof of $ A^\circ \subseteq B^\circ $**To prove: $ A^\circ \subseteq B^\circ $Given:1. $ A^\circ \subseteq A $2. $ B^\circ \subseteq B $To show:1. $ A^\circ \subseteq A \subseteq B \supseteq B^\circ $2. Hence, $ A^\circ \subseteq B^\circ $Conclusion:Since $ A^\circ $ is a subset of $ B^\circ $ through intermediary subsets, the proof is complete.

Name: I think I am on the right track but I might be wrong. The work provide
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Description: I think I am on the right track but I might be wrong. The work provided is what I have done. Let $ (X, \mathcal{T}) $ be a topological space and suppose that $ A $ and $ B $ are subsets of $ X $ such that $ A \subseteq B $. Prove that \( A^

Let x ∈A°. Then by definition, there exists an open set U such that x∈U⊆A.Since A⊆B hence x∈U⊆B ,…

Answered: Let (X, I) be a topological space and…

Math

Advanced Math

Let (X, I) be a topological space and suppose that A and B are subsets of X such that ACB. Prove that A° C B° and ACB.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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