Continuous mappings | General topology | Lemmas
In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function is open if for any open set in the image is open in Likewise, a closed map is a function that maps closed sets to closed sets. A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa. Open and closed maps are not necessarily continuous. Further, continuity is independent of openness and closedness in the general case and a continuous function may have one, both, or neither property; this fact remains true even if one restricts oneself to metric spaces. Although their definitions seem more natural, open and closed maps are much less important than continuous maps. Recall that, by definition, a function is continuous if the preimage of every open set of is open in (Equivalently, if the preimage of every closed set of is closed in ). Early study of open maps was pioneered by Simion Stoilow and Gordon Thomas Whyburn. (Wikipedia).
From playlist Open Q&A
Closed Intervals, Open Intervals, Half Open, Half Closed
00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation
From playlist Calculus
All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an
From playlist Real Analysis
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
Open Source vs. Closed Source Software
In this video, you’ll learn more about the differences between open-source software and closed-source software. Visit https://edu.gcfglobal.org/en/basic-computer-skills/ for more technology, software, and computer tips. We hope you enjoy!
From playlist Technology Trends
An Example of a Closed Continuous Function that is Not Open
An Example of a Closed Continuous Function that is Not Open If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
Infinite Intersection of Open Sets that is Closed Proof
Infinite Intersection of Open Sets that is Closed Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
Intro to Open Sets (with Examples) | Real Analysis
We introduce open sets in the context of the real numbers, along with examples and nonexamples of open sets. This is an important topic in the topology of the reals. We say a subset U of the reals is open if, for any x in U, there exists a delta-neighborhood of x that is contained in U. We
From playlist Real Analysis
Talking to Your Computer with OpenAI Codex
Learn more: https://openai.com/blog/openai-codex
From playlist OpenAI Codex
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?
MAST30026 Lecture 12: Function spaces (Part 2)
The aim of this lecture was to motivate the definition of the compact-open topology on function spaces, via the adjunction property. I explained how any topology making the adjunction property true must include a certain class of open sets, which we will define next lecture to be a sub-bas
From playlist MAST30026 Metric and Hilbert spaces
CTNT 2022 - An Introduction to Galois Representations (Lecture 2) - by Alvaro Lozano-Robledo
This video is part of a mini-course on "An Introduction to Galois Representations" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)
What is a Manifold? Lesson 4: Countability and Continuity
In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.
From playlist What is a Manifold?
Algebraic Topology - 1 - Compact Hausdorff Spaces (a Review of Point-Set Topology)
This is mostly a review point set topology. In general it is not true that a bijective continuous map is invertible (you need to worry about the inverse being continuous). In the case that your spaces are compact hausdorff this is true! We prove this in this video and review necessary fac
From playlist Algebraic Topology
Schemes 21: Separated morphisms
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We define separated and quasi-separated schemes and morphisms, give a few examples, and show that if a scheme has a separated morphism to an affine scheme the
From playlist Algebraic geometry II: Schemes
Tony Yue Yu - 3/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Notes: https://nextcloud.ihes.fr/index.php/s/pSQnsgx72a4S5zj 3/4 - Naive counts, tail conditions and deformation invariance. --- We show that the naive counts of rational curves in an affine log Calabi-Yau variety U, containing an open algebraic torus, determine in a surprisingly simple w
From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Weil conjectures 7: What is an etale morphism?
This talk explains what etale morphisms are in algebraic geometry. We first review etale morphisms in the usual topology of complex manifolds, where they are just local homeomorphism, and explain why this does not work in algebraic geometry. We give a provisional definition of etale morphi
From playlist Algebraic geometry: extra topics
Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=G3mAXHuoDSw&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Intersection and union of sets 2
drawing intersection and union with geogebra. this video can help you to drawing sets.
From playlist Go Geogebra