Theorem B.ToJ (properies of closure)let(X,d) be a metric space and AB. Bubbed of xG) ACB→ d(A) cd(B)O d(d(A) =d(A)[ Soi d(A) isclosed set]O AcB and B is closed J → d(A) CB[S0: d(A) is the Bma llest closed set]- pro ve the abo ve proper hes OD, (using thewritfing style of the Model Profs.Hint: for @ only need to prove d( d(A)) e dCA)Use charc tirization withopen balls: xed(d(A))E 13 Ca ,r )

Let X,d be a metric space and A, B⊆X. We will use the following in the proofs, Definition of clA:…

Answered: let Qid) be a metric space and AiB…

let Qid) be a metric space and AiB Bubeet of x ACB = d(A) cd(B) [ Soi d(A) is closed set] P B is closed J→ d(A) CB AcB and

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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Theorem B.ToJ (properies of closure)
let
(X,d) be a metric space and AB. Bubbed of x
G) ACB
→ d(A) cd(B)
O d(d(A) =d(A)
[ Soi d(A) is
closed set]
O AcB and B is closed J → d(A) CB
[S0: d(A) is the Bma llest closed set]
- pro ve the abo ve proper hes OD, (
using the
writfing style of the Model Profs.
Hint: for @ only need to prove d( d(A)) e dCA)
Use charc tirization with
open balls: xed(d(A))
E 13 Ca ,r )

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