In topology, the Sorgenfrey plane is a frequently-cited counterexample to many otherwise plausible-sounding conjectures. It consists of the product of two copies of the Sorgenfrey line, which is the real line under the half-open interval topology. The Sorgenfrey line and plane are named for the American mathematician Robert Sorgenfrey. A basis for the Sorgenfrey plane, denoted from now on, is therefore the set of rectangles that include the west edge, southwest corner, and south edge, and omit the southeast corner, east edge, northeast corner, north edge, and northwest corner. Open sets in are unions of such rectangles. is an example of a space that is a product of Lindelöf spaces that is not itself a Lindelöf space. The so-called anti-diagonal is an uncountable discrete subset of this space, and this is a non-separable subset of the separable space . It shows that separability does not inherit to closed subspaces. Note that and are closed sets; it can be proved that they cannot be separated by open sets, showing that is not normal. Thus it serves as a counterexample to the notion that the product of normal spaces is normal; in fact, it shows that even the finite product of perfectly normal spaces need not be normal. (Wikipedia).
Big Plane vs Little Plane (The Economics of Long-Haul Flights)
Sign up for a 30 day Audible free trial: http://www.Audible.com/Wendover Support Wendover Productions on Patreon: http://Patreon.com/WendoverProductions Apply to animate for Wendover Productions: http://www.wendoverproductions.com/apply-to-animate Airbus made an enormous plane, Boeing m
From playlist Transportation/Travel Videos
4 Giant Aircrafts in the World
Some of the aircrafts are remarkable in terms of their huge size. One of the biggest ones is the Boeing 787-10 Dreamliner. It is an American wide body jet airliner. It is 223ft (68m) long and its wingspan is 196ft (60m) wide. It is so comfortable that you can sit in large seats. The s
From playlist Giant Machines
NATO Airshow At Soesterberg (1953)
Unused / unissued footage - dates and locations may be unclear or unknown. NATO (North Atlantic Treaty Organisation) Airshow at Soesterberg, Holland / Netherlands. (Natural sound of planes throughout.) General view of spectators at Soesterberg. Flags of NATO countries. Formation o
From playlist NATO
The Sopwith Snipe - WW1 Pilot's Gear I THE GREAT WAR Special
Play Warthunder For Free: https://warthunder.com/play4free?r=greatwar Indy takes a look at the Sopwith Snipe and meets Trevor who shows us the typical gear of a WW1 pilot. » HOW CAN I SUPPORT YOUR CHANNEL? You can support us by sharing our videos with your friends and spreading the word
From playlist SPECIAL EPISODES - The Great War
How The Special Forces Transport Their Displays and Prop Signs
The new generation of special SOF land vehicles are as cool as they come. Special forces require vehicles that can assist them in their clandestine and sometimes action-packed operations. These can range from the M1297 Army Ground Mobility Vehicle to the Christini AWD military motorbike.
From playlist Military Mechanics
Please support us at Patreon.com so that we can add one more member to the team and will be able to release 2 educational videos/month. https://www.patreon.com/LearnEngineering Helicopters are the true flying machines. They can take off and land without the need for a runway. They can ho
From playlist Aerospace & Aeronautical
How do airplanes fly? It's not magic. Learn about the forces that help (and hinder) airplane flight. License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Things that Fly!
New official movie "Flyboard Family" by Zapata Racing and Friends more informations please contact zapata-racing.com Zapata Racing is proud to introduce you the video of the first flyboard® world cup Click on this link http://youtu.be/BkZ8euApHRo
From playlist Forces
Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007
Lecture 04: Square systems; equations of planes. View the complete course at: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.02 Multivariable Calculus, Fall 2007
Points, Lines, Planes, Segments, & Rays - Collinear vs Coplanar Points - Geometry
This geometry video tutorial provides a basic introduction into points, lines, segments, rays, and planes. It explains how to identify three collinear points and how to distinguish it from noncollinear points. It explains the difference between coplanar points and noncoplanar points. Th
From playlist Geometry Video Playlist
Advanced ceramics for strategic applications by Prof. H.S. Maiti,Department of Metallurgy and Material Science,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Advanced Ceramics for Strategic Applications | CosmoLearning.org Materials Science
MIT 3.60 | Lec 6a: Symmetry, Structure, Tensor Properties of Materials
Part 1: 2D Plane Groups, Lattices (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
WildLinAlg10: Equations of lines and planes in 3D
This video shows how we work with lines in the plane and planes in 3D space in Linear Algebra. A line in 2D is represented by a linear equation in x and y, a plane in 3D by a linear equation in x,y and z. Both can also be described in parametric form. It is important to be able to change f
From playlist A first course in Linear Algebra - N J Wildberger
5: Equations of Planes - Valuable Vector Calculus
Explanation of the dot product: https://youtu.be/y-kafkvDkFg Explanation of the cross product: https://youtu.be/RecUff64IX0 Planes are an important part of vector calculus, and we need to know how to describe planes with equations and vectors. This is where our knowledge of the dot produ
From playlist Valuable Vector Calculus
Introduction to Solid State Physics, Lecture 8: Reciprocal Lattice
Upper-level undergraduate course taught at the University of Pittsburgh in the Fall 2015 semester by Sergey Frolov. The course is based on Steven Simon's "Oxford Solid State Basics" textbook. Lectures recorded using Panopto, to see them in Panopto viewer follow this link: https://pitt.host
From playlist Introduction to Solid State Physics
What are Planar Graphs? | Graph Theory
What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t
From playlist Graph Theory
MIT 3.60 | Lec 6b: Symmetry, Structure, Tensor Properties of Materials
Part 2: 2D Plane Groups, Lattices (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
Briefing eines Bombenangriffs, US-Air Force Piloten planen Luftangriff auf Deutschland
US-Piloten sitzen auf dem Rollfeld eines Flugplatzes und werden auf einen Angriff vorbereitet, den sie fliegen werden. Im Hintergrund sieht man P-51 Mustang Flugzeuge.
From playlist Footage
Equations of planes | MIT 18.02SC Multivariable Calculus, Fall 2010
Equations of planes Instructor: Joel Lewis View the complete course: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.02SC: Homework Help for Multivariable Calculus