3. Prove that if G is an open set dense in the metric space (S, d)then SG is nowhere dense in S.4. Prove that if Gn is an open set which is dense in the completemetric space (S, d) for n = 1,2,... then n₁ G₁ is dense in S.

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3. Prove that if G is an open set dense in the metric space (S, d) then SG is nowhere dense in S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 8E: Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg,...

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3. Prove that if G is an open set dense in the metric space (S, d)
then SG is nowhere dense in S.
4. Prove that if Gn is an open set which is dense in the complete
metric space (S, d) for n = 1,2,... then n₁ G₁ is dense in S.

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