General topology

Development (topology)

In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms. Let be a topological space. A development for is a countable collection of open coverings of , such that for any closed subset and any point in the complement of , there exists a cover such that no element of which contains intersects . A space with a development is called developable. A development such that for all is called a nested development. A theorem from Vickery states that every developable space in fact has a nested development. If is a refinement of , for all , then the development is called a refined development. Vickery's theorem implies that a topological space is a Moore space if and only if it is regular and developable. (Wikipedia).

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Topology (What is a Topology?)

What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b

From playlist Topology

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Topology 1.3 : Basis for a Topology

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From playlist Topology

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The Generalized Neighborhood Base Construction

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From playlist The CHALKboard 2022

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From playlist Topology

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Topology 1.4 : Product Topology Introduction

In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology

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Topology 1.1 : Open Sets of Reals

In this video, I give a definition of the open sets on the real numbers. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology

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Definition of a Topological Space

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space

From playlist Topology

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From playlist Topology & Manifolds

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Kathryn Hess interviewed by Peter Bubenik (August 11, 2021)

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From playlist AATRN Interviews

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John Milnor - The Abel Prize interview 2011

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From playlist The Abel Prize Interviews

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Sir Michael Atiyah - The Mysteries of Space [1991]

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From playlist Mathematics

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Michael Atiyah: Poincaré conjecture, Hodge conjecture, Yang-Mills, Navier-Stokes [2000]

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From playlist Introduction to Homotopy Theory

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From playlist Mathematics

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Adam Topaz - The Liquid Tensor Experiment - IPAM at UCLA

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From playlist 2023 Machine Assisted Proofs Workshop

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Compactness

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From playlist Topology

Related pages

Topological space | Regular space | Complement (set theory) | Counterexamples in Topology | Moore space (topology) | Separation axiom | Topology | Refinement (topology)