In functional analysis, an F-space is a vector space over the real or complex numbers together with a metric such that 1. * Scalar multiplication in is continuous with respect to and the standard metric on or 2. * Addition in is continuous with respect to 3. * The metric is translation-invariant; that is, for all 4. * The metric space is complete. The operation is called an F-norm, although in general an F-norm is not required to be homogeneous. By translation-invariance, the metric is recoverable from the F-norm. Thus, a real or complex F-space is equivalently a real or complex vector space equipped with a complete F-norm. Some authors use the term Fréchet space rather than F-space, but usually the term "Fréchet space" is reserved for locally convex F-spaces. Some other authors use the term "F-space" as a synonym of "Fréchet space", by which they mean a locally convex complete metrizable topological vector space. The metric may or may not necessarily be part of the structure on an F-space; many authors only require that such a space be metrizable in a manner that satisfies the above properties. (Wikipedia).
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
The formal definition of a vector space.
From playlist Linear Algebra Done Right
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From playlist Science Unplugged: Special Relativity
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
A01 An introduction to a series on space medicine
A new series on space medicine.
From playlist Space Medicine
Metric Spaces - Lectures 5 & 6: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 3rd of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Part III: Linear Algebra, Lec 4: Linear Transformations
Part III: Linear Algebra, Lecture 4: Linear Transformations Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Calculus of Complex Variables
Jayce Getz: New avenues for the circle method, Lecture IV
Motivated by research arising from automorphic representation theory, I will present some ideas that should open up new avenues of research in the circle method. In the first half of the lectures I will discuss an adelic version of the delta-method of Duke, Friedlander, Iwaniec and Heath-B
From playlist Hausdorff School "The Circle Method"
What is a Manifold? Lesson 15: The cylinder as a quotient space
What is a Manifold? Lesson 15: The cylinder as a quotient space This lesson covers several different ideas on the way to showing how the cylinder can be described as a quotient space. Lot's of ideas in this lecture! ... too many probably....
From playlist What is a Manifold?
What is a Riesz Space? -- MathMajor Seminar
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From playlist MathMajor Seminar
Metric Spaces - Lectures 9 & 10: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 5th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Metric Spaces - Lectures 13 & 14: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 7th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
MAST30026 Lecture 13: Metrics on function spaces (Part 2)
I discussed pointwise and uniform convergence of functions, proved that the uniform limit of continuous functions is continuous, and used that to prove that Cts(X,Y) is a complete metric space with respect to the sup metric if X is compact and Y is a complete metric space. Lecture notes:
From playlist MAST30026 Metric and Hilbert spaces
Metric Spaces - Lectures 21, 22 & 23: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 11th of 11 videos. The course is about the notion of distance. You m
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Definition of linear map. Algebraic properties of linear maps.
From playlist Linear Algebra Done Right
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. Given a continuous map between topological spaces there are two natural ways to transfer sheaves from one space to another. We summarize the main properties of
From playlist Algebraic geometry II: Schemes