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Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite Prove $φ(R^2)$ is a smooth surface and $φ(u,v)=(vcos u,vsin u,bu)$ $R^2rightarrow R^3$ and b>0 constant. Its rank $Dφ$ is 2, so I'm ok with that part. Only thing to prove is that it has an continuous inverse so $φ$ can be an acceptable parametrization. Can i just argue the topology definition . I know the existence of the inverse hence if the pre image of the inverse of open sets of$ R^2$ are open in $R^3$ then the inverse is continuous.But still that needs proof calculus differential-geometry surfaces share | cite | improve this question edited Sep 3 at 14:49 asked Sep 3 at 14:05 Manolis Lyviakis 1,307 6 25 It makes little sense to say "where $varphi$ is a smooth function" and then to define it explicitly. – amsmath Sep 3 at 14:08 thats how the problem was presented . I know its a redundancy. – Manolis Lyviakis S

Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite Please tell me how to solve the following exercise which is in the book "Conceptual Mathematics A first introduction to categories Second Edition". How can I show that for any object X of category of graphs the diagram is commutative from the fact that following two diagrams are commutative? category-theory share | cite | improve this question edited Sep 3 at 14:22 Arnaud D. 14.9k 5 21 42 asked Sep 3 at 13:54 konyonyo 10 3 Welcome to MathStackExchange. It is generally recommended to avoid pointing to images with texts and prints from books, and rather retype everything here. This helps this site to become more self-contained, and shows some work. It is also good practice to re-state the problem in your own words (as it's helpful on its own, and may reveals where your lack of understanding is). If you've made any attempt on solving the exercise,