Theorem (Axioms of an interior): Let (M, d) be a metric space and S,TCM. Then:(1) Ø° = Ø and M° = M.(2) If SCT, then S° ST.(4) S is open if, and only if, S = S(5) S° = S°.(7) In general, S° UT S (SUT)', but (S U T) S° UT°.

As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Answered: (1) Ø° = Ø and M° = M. (2) If SST, then…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 67E

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(1) Ø° = Ø and M° = M. (2) If SST, then S° ST°. (4) S is open if, and only if, S = S