Scheme theory | Wellfoundedness | Algebraic geometry | Properties of topological spaces
In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the complements of the closed subsets. The Noetherian property of a topological space can also be seen as a strong compactness condition, namely that every open subset of such a space is compact, and in fact it is equivalent to the seemingly stronger statement that every subset is compact. (Wikipedia).
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
Noetherianity up to Symmetry - Jan Draisma
Members' Colloquium Topic: Noetherianity up to Symmetry Speaker: Jan Draisma Affiliation: Member, School of Mathematics Date: October 17, 2022 Noetherianity is a fundamental property of modules, rings, and topological spaces that underlies much of commutative algebra and algebraic geomet
From playlist Mathematics
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
algebraic geometry 6 Noetherian spaces
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers Noetherian rings, Noetherian spaces, and irreducible sets.
From playlist Algebraic geometry I: Varieties
Schemes 15: Quasicompact, Noetherian
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define quasi-compact, Noetherian, and locally Noetherian schemes, give a few examples, and show that "locally Noetherian" is a local property.
From playlist Algebraic geometry II: Schemes
Commutative algebra 5 (Noetherian rings)
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 find three equivalent ways of defining Noetherian rings, and give several examples of Noetherian and non-No
From playlist Commutative algebra
Commutative algebra 36 Artin Rees lemma
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 state and prove the Artin-Rees lemma, which states that the restriction of an stable I-adic filtration (of
From playlist Commutative algebra
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Commutative algebra 55: Dimension of local rings
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. We give 4 definitions of the dimension of a Noetherian local ring: Brouwer-Menger-Urysohn dimension, Krull dimension, degree o
From playlist Commutative algebra
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
Ofer Gabber - Spreading-out of rigid-analytic families and observations on p-adic Hodge theory
(Joint work with Brian Conrad.) Let K be a complete rank 1 valued field with ring of integers OK, A an adic noetherian ring and f: A→OK an adic morphism. If g: X→Y is a proper flat morphism between rigid analytic spaces over Kthen locally on Y a flat formal model of gspreads out to a prope
From playlist Conférences Paris Pékin Tokyo
Noether's works in Topology by Indranil Biswas
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
Symmetries and Condensed Matter physics by Subhro Bhattacharya
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether