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Analysis and Geometry in Metric Spaces

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MATH3961/4061 Metric Spaces (Advanced)

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1. Introduction and Basic Definitions

Course content Course content. Metric spaces and continuity This free course is available to start right now. Free course Metric spaces and continuity.

Conclusion Following completion of this free OpenLearn course, Metric spaces and continuity , as well as being able to understand the terms and definitions, and use the results introduced, you should also find that your skills and confidence in reading, understanding and writing mathematical arguments are improving. You should now be able to: understand the Euclidean distance function on R n and appreciate its properties, and state and use the Triangle and Reverse Triangle Inequalities for the Euclidean distance function on R n explain the definition of continuity for functions from R n to R m and determine whether a given function from R n to R m is continuous explain the geometric meaning of each of the metric space properties M1 — M3 and be able to verify whether a given distance function is a metric distinguish between open and closed balls in a metric space and be able to determine them for given metric spaces define convergence for sequences in a metric space and determine whether a given sequence in a metric space converges state the definition of continuity of a function between two metric spaces.

Analysis and Geometry in Metric Spaces | Directory of Open Access Journals

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The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. Mathematical Logic Quarterly Volume 64, Issue Kyriakos Keremedis Corresponding Author E-mail address: kker aegean. Read the full text. Tools Request permission Export citation Add to favorites Track citation.

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  5. Volume 64 , Issue April Pages Related Information. Close Figure Viewer. Browse All Figures Return to Figure.