Kleinian groups | Compactness theorems | Riemann surfaces
In mathematics, Mumford's compactness theorem states that the space of compact Riemann surfaces of fixed genus g > 1 with no closed geodesics of length less than some fixed ε > 0 in the Poincaré metric is compact. It was proved by David Mumford as a consequence of a theorem about the compactness of sets of discrete subgroups of semisimple Lie groups generalizing Mahler's compactness theorem. (Wikipedia).
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
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Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
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Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Math 131 Fall 2018 100818 Limits and Continuity in Metric Spaces
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From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
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From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
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From playlist Course 6: Introduction to Analysis
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From playlist Mathematics
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From playlist Course 6: Introduction to Analysis
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From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
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David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
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From playlist Ecole d'été 2019 - Foliations and algebraic geometry
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Mark McLean Stony Brook University April 4, 2014 Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold calle
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Thanks for watching! Go check out all submissions to 3blue1brown's contest: https://3b1b.co/SoME1 Corrections and remarks: none yet, let me know in the comments if you have any. Sources and resources: – First-order logic, compactness theorem David Marker's book: https://www.springer.com
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