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# Let A â‚¬ R2. Let B â‚¬ R be defined by B = {x â‚¬ R there is y â‚¬ R such that (x,Y) â‚¬ A}_B is called the projection of A onto the x-axis_ (a...

## Question

###### Let A â‚¬ R2. Let B â‚¬ R be defined by B = {x â‚¬ R there is y â‚¬ R such that (x,Y) â‚¬ A}_B is called the projection of A onto the x-axis_ (a) If A is a closed set in R2, is B necessarily a closed set in R? (b) If A is an open set in R2,is B necessarily an open set in R?

Let A â‚¬ R2. Let B â‚¬ R be defined by B = {x â‚¬ R there is y â‚¬ R such that (x,Y) â‚¬ A}_ B is called the projection of A onto the x-axis_ (a) If A is a closed set in R2, is B necessarily a closed set in R? (b) If A is an open set in R2,is B necessarily an open set in R?

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