MathematicalPhysicist

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## Main Question or Discussion Point

Im reviewing material for the exam and came across this question:

Let pi_1:RxR->R be the projection on the first coordinate.

Let A be the subspace of RxR consisitng of all points (x,y) s.t either x>=0 or (inclusive or) y=0.

let q:A->R be obtained by resticting pi_1. show that q is quotient map that is neither open nor closed.

now to show that it's quotient map is the easy task, I want to see if I grasp it correctly, the set [0,infinity)x{0} is closed and open in A, but q([0,infinity)x{0})=[0,infinity) isn't closed nor open in R, correct?

Let pi_1:RxR->R be the projection on the first coordinate.

Let A be the subspace of RxR consisitng of all points (x,y) s.t either x>=0 or (inclusive or) y=0.

let q:A->R be obtained by resticting pi_1. show that q is quotient map that is neither open nor closed.

now to show that it's quotient map is the easy task, I want to see if I grasp it correctly, the set [0,infinity)x{0} is closed and open in A, but q([0,infinity)x{0})=[0,infinity) isn't closed nor open in R, correct?