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If f and g be continuous real valued functions on the metric space M. Let A be the set of all x ∈ M s.t. f(x) < g(x)
  • a)
     A is closed 
  • b)
     A is open 
  • c)
     Neither open nor closed 
  • d)
     None of these 
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If f and g be continuous real valued functions on the metric space M. ...
It is a very well known theorem that if f and g be continuous real – valued function on the metric space M and A be the set of all x ∈ M s.t. f(x) < g(x) then A is open set. 
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If f and g be continuous real valued functions on the metric space M. Let A be the set of all x ∈ M s.t. f(x) < g(x)a)A is closedb)A is openc)Neither open nor closedd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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