# r^n is complete

If a (distance) metric on a connected Riemannian manifold locally agrees with the Riemannian metric, is it equal to the induced metric? Computations with the distance function on a Riemannian manifold, Riemannian distance functions on the real line, Square of the distance function on a Riemannian manifold. Why did mainframes have big conspicuous power-off buttons? What characters can be used for up/down triangle (arrow without stem) for display in HTML? Thus the graph is now (c − 1)-coloured. by LF (CR+LF, '\r\n', 0x0D0A). @David But I was wondering that effect of, @DanielMošmondor Alternatively, you could just remember that order is impoRtaNt. Add Website Suggest an Edit. In fact I would advise not doing this at all. bring to a whole, with all the necessary parts or elements; "A child would complete the family" come or bring to a finish or an end; "He finished the dishes"; "She completed the requirements for her Master's Degree"; "The fastest runner finished the … Complete your bachelor's degree in nursing with 100% online classes through our R.N. At the moment I don't see why that sould be the case, but I cannot construct a counter-example. Now 'go colour-blind' and pretend that c − 1 and c are the same colour. Examples of back of envelope calculations leading to good intuition? In C#, should I use string.Empty or String.Empty or “” to intitialize a string? Unix (and hence Linux as well) Unix uses a single '\n' to indicate a new line. Or that you. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. When in doubt, use any freeware hex viewer/editor to see how a file encodes its new line. @RobKennedy haha you know I came here and read about return, and thought "great!". Choose the metric such that $G$ equals the usual Euclidian metric everywhere except $\bigcup K_n$ where $K_n$ is the ball with radius $1/n$ around $p_n$. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Making statements based on opinion; back them up with references or personal experience. Prove that R^n is a complete metric space. @Daniel: I should have been more specific. From Wikipedia (you can read which is correct for your OS at that article): Systems based on ASCII or a compatible Be careful with doing this manually. Take hyperbolic $n$-space, which is complete and diffeomorphic to $\mathbb{R}^n$ but not bi-Lipschitz to it. What are the correct version numbers for C#? https://ccrma.stanford.edu/~craig/utility/flip/, How to write an effective developer resume: Advice from a hiring manager, Podcast 290: This computer science degree is brought to you by Big Tech, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, Congratulations VonC for reaching a million reputation. They expect a newline to be the combination of two characters, namely '\r\n' (or 13 followed by 10). Find words with any set of letters. Please contact the business for updated hours/services due to the COVID-19 advisory. Or that when you asked at SO someone gave you a RemiNder, which you later forgot. Regex to match string literal with newline and carriage return. Therefore our de nition of a complete metric space applies to normed vector spaces: an n.v.s. Tomorrow: 8:00 am - 5:00 pm. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. MathJax reference. I'd use the word 'return' to remember, the r comes before the n. If you are using C# you should use Environment.NewLine, which accordingly to MSDN it is: A string containing "\r\n" for non-Unix platforms, or a string containing "\n" for Unix platforms. What is the minimum assumption on $G$ such that the manifold $\mathbb{R}^n$ is complete as a metric space with respect to the Riemannian distance determined by $G$.