In mathematics, a space is a set (sometimes called a universe) with some added structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can be elements of a set, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space. More precisely, isomorphic spaces are considered identical, where an isomorphism between two spaces is a one-to-one correspondence between their points that preserves the relationships. For example, the relationships between the points of a three-dimensional Euclidean space are uniquely determined by Euclid's axioms, and all three-dimensional Euclidean spaces are considered identical. Topological notions such as continuity have natural definitions in every Euclidean space. However, topology does not distinguish straight lines from curved lines, and the relation between Euclidean and topological spaces is thus "forgetful". Relations of this kind are treated in more detail in the Section . It is not always clear whether a given mathematical object should be considered as a geometric "space", or an algebraic "structure". A general definition of "structure", proposed by Bourbaki, embraces all common types of spaces, provides a general definition of isomorphism, and justifies the transfer of properties between isomorphic structures. (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
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
"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://twitter.com/worldscienceu"
From playlist Science Unplugged: Special Relativity
Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?
From playlist Guide to Space
A01 An introduction to a series on space medicine
A new series on space medicine.
From playlist Space Medicine
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Astronomy - Ch. 31: What is Space Made of? (6 of 15) Einstein Quotes & Other Thoughts
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn some of Michel van Biezen, Einstein, and other thoughts of What is Space Made of? Next video in this series can be see
From playlist ASTRONOMY 31 WHAT IS SPACE MADE OF?
Lecture with Ole Christensen. Kapitler: 00:00 - Introduction; 06:45 - Vector Spaces; 07:15 - Example 1; 12:00 - Mathematical Tool - Fourier Transform; 17:00 - Example 2; 20:00 - Example 3; 23:00 - New Concept - Norm; 27:45 - Lemma 2.1.2 - The Opposite Triangle Inequality; 35:15 - Convergen
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Wolfram Science Initiatives Update (September 15, 2022)
Join Stephen Wolfram as he discusses updates on the Physics Project, the Ruliad, Multicomputation, and Metamathematics! If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfr
From playlist Science and Research Livestreams
Porque não conseguimos ver para além das três dimensões — Rogério Martins — ICM2018
Portuguese mathematician Rogério Martins is a professor at the University of Lisbon. He is a well-known researcher in Differential Equations and Dynamical Systems. Martins is also the presenter and mastermind of “Isto é Matemática” ("This is Mathematics"), a TV show for the dissemination
From playlist Public Lectures
Wolfram Physics Project: Working Session Thursday, July 23, 2020 [Metamathematics | Part 1]
This is a Wolfram Physics Project progress update at the Wolfram Summer School. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physics-announce
From playlist Wolfram Physics Project Livestream Archive
Topology Without Tears - Video 4d - Writing Proofs in Mathematics
This is part (d) of the fourth video in a series of videos which supplement my online book "Topology Without Tears" which is available free of charge at www.topologywithouttears.net Video 4 focusses on the extremely important topic of writing proofs. This video is about Mathematical Induc
From playlist Topology Without Tears
Wolfram Physics Project: a Conversation on Current Work (Jan. 26, 2021)
This is a Wolfram Physics Project conversation on our continuing efforts to make progress on the fundamental theory of physics. Begins at 3:00 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Ch
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Working Session Tuesday, Nov. 16, 2021 [Metamathematics]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Max Tegmark - Is Mathematics Invented or Discovered?
Free access Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music? Or is mathematics dis
From playlist Closer To Truth - Max Tegmark Interviews
IMPA in a context of international reconfiguration of mathematics – T. Roque – ICM2018
History of Mathematics Invited Lecture 19.3 IMPA’s coming of age in a context of international reconfiguration of mathematics Tatiana Roque Abstract: In the middle of the 20^{th} century, the intimate link between science, industry and the state was stimulated, in its technical-scientifi
From playlist History of Mathematics
Quantum Mathematics and the Fate of Space, Time and Matter - Robbert Dijkgraaf
The elementary particles that make up the bizarre quantum world not only represents a more fundamental description of nature, they also inspires a new realm of mathematics that might be called "quantum mathematics." This turns out to be a powerful tool to solve deep outstanding mathematica
From playlist Mathematics Research Center
Can you Actually Stretch Space? Part I (How do you Describe Space?)
Before we can talk about how to Stretch Space we first must be able to Describe Space!
From playlist Summer of Math Exposition Youtube Videos