Prove the set $leftvecxinmathbbR^n : 0 < x_i < 1, 1leq i leq nright$ is open. The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Prove that any subset of $mathbbR^2$ which is $D$-open is also $D_1$-open.Prove that a set is openShow a set is open using open ballsHelp with proving triangle law to prove these distance functions are metric spacesProve this set is open in $mathbbR^n$Prove that $g(x,y) = left((x,y), (x,y)right)$ is continuous.Properties of $d(x,y) = vert x_1 - y_1vert^frac12 + vert x_2-y_2vert^frac12$Prove that the set $A=(x,y)inmathbbR^2: x^2 + y^2 > 4, y < 6$ is open in $mathbbR^2$Prove that $N((0,0);1)$ is an open set in $mathbbRtimesmathbbR$ with metric $d((x_1,x_2),(y_1,y_2))=|x_1-y_1|+|x_2-y_2|$.Determine whether the following subsets of $mathbbR^2$ are open with respect to the metric $d$.
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