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
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
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
A Set is Closed iff it Contains Limit Points | Real Analysis
We prove the equivalence of two definitions of closed sets. We may say a set is closed if it is the complement of some open set, or a set is closed if it contains its limit points. These definitions are equivalent, so we'll prove a set is closed if and only if it contains its limit points.
From playlist Real Analysis
Closure of Sets (Allegra's Question)
clarifying the idea of closure of a set under an operation
From playlist Middle School This Year
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
Finding Closed Sets, the Closure of a Set, and Dense Subsets Topology
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding Closed Sets, the Closure of a Set, and Dense Subsets Topology
From playlist Topology
SET is an awesome game that really gets your brain working. Play it! Read more about SET here: http://theothermath.com/index.php/2020/03/27/set/
From playlist Games and puzzles
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Real Analysis Ep 15: Closure of a set
Episode 15 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about the closure of a set. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.f
From playlist Math 3371 (Real analysis) Fall 2020
Proof for Unions and Intersections of Closed Sets | Real Analysis
We prove the intersection of an arbitrary collection of closed sets is closed, and the union of a finite collection of closed sets is closed. To do this, we use DeMorgan's Laws, the definition of closed and open sets, and previously proven results on the unions and intersections of open se
From playlist Real Analysis
Real Analysis Ep 14: Closed sets
Episode 14 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about closed sets of real numbers. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://f
From playlist Math 3371 (Real analysis) Fall 2020
Real Analysis Ep 18: Compact sets
Episode 18 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about compact sets. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.fairfield
From playlist Math 3371 (Real analysis) Fall 2020
How to Identify the Elements of a Set | Set Theory
Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times
From playlist Set Theory
The topology of metric spaces -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Commutative algebra 15 (Noetherian spaces)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we define Noetherian topological spaces, and use them to show that for a Noetherian ring R, every closed subse
From playlist Commutative algebra
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory