The term "local property" can refer to different concepts depending on the context in which it is used. Here are a few interpretations of "local property": 1. **Real Estate Context**: In real estate, local property may refer to real estate assets that are situated in a specific geographic area. This can involve considerations like property value, market trends, zoning laws, and community characteristics that pertain to that specific locality.
José Adem was a notable Mexican mathematician, recognized for his contributions to topology and functional analysis. Born on April 24, 1918, in Mexico City, he made significant advancements in the field of mathematics and played a crucial role in the development of mathematical research in Mexico. Adem is particularly known for the Adem relations in algebraic topology and for his work on the cohomology of various mathematical structures.
In mathematics, the term "net" can refer to several different concepts, depending on the context. Here are two of the most common interpretations: 1. **Net in Topology**: In topology, a net is a generalization of a sequence that allows the indexing of elements by a directed set. While a sequence is indexed by the natural numbers, a net can be indexed by any directed set, which gives it more flexibility.
In the field of topology, a pretopological space is a generalization of the concept of a topological space. While the standard definition of a topological space involves a set along with a topology (a collection of open sets that satisfy certain axioms), a pretopological space relaxes some of these requirements.
Hyperbolic Dehn surgery is a technique in the study of 3-manifolds, primarily in the field of low-dimensional topology. It involves a process of modifying a given three-dimensional manifold by removing a solid torus and gluing it back in a different way, thus altering the topology of the manifold.
A hyperbolic 3-manifold is a type of three-dimensional manifold that possesses a geometry modeled on hyperbolic space. Specifically, a hyperbolic 3-manifold is characterized by having a constant negative curvature, which means that its geometric properties are governed by hyperbolic geometry, rather than Euclidean or spherical geometries.
"Dogbone space" typically refers to a specific type of topological space or geometric structure featuring a shape resembling a dog bone. In a more formal mathematical context, the term may arise in discussions of topology, particularly in relation to shape theory, homotopy theory, or specific constructions in algebraic topology. The "dogbone" shape usually consists of a central narrowing region with two enlarged ends.
"Bing shrinking" refers to a phenomenon where Microsoft's Bing search engine experiences a decline in its market share or usage compared to its competitors, particularly Google. This can happen due to factors such as user preference, changes in search algorithms, or improvements in competitors' services. The term may also pertain to specific features or services within Bing being scaled back or removed.
A **branched surface** is a concept in topology that can be thought of as a surface that has branching structures or singular points, where the usual notion of a smooth manifold breaks down. More specifically, branched surfaces arise in the study of topology and geometric structures where traditional structures—such as smooth surfaces—may not be adequate to describe certain features or behaviors.
The Geometrization Conjecture is a fundamental concept in the field of 3-manifold topology, proposed by mathematician William Thurston in the late 20th century. It asserts that every closed, orientable 3-manifold can be decomposed into pieces that each have one of a specific set of geometric structures. These structures correspond to eight possible geometries that can be assigned to a manifold.
A Klein bottle is a non-orientable surface with no distinct "inside" or "outside." It is a mathematical object in topology, a branch of mathematics concerned with the properties of space that are preserved under continuous transformations.
A Cloud-Native Network Function (CNF) refers to a software-based network function that is designed to run in a cloud-native environment, leveraging containerization, microservices architecture, and orchestration technologies. CNFs are an evolution of traditional network functions, such as firewalls, routers, and load balancers, which were typically implemented as dedicated hardware appliances or virtual machines.
In networking, a "feeder line" typically refers to a connection that carries data or signals from a primary source to a secondary node or device. The term can be applied in various contexts, including telecommunications, computer networks, and even energy distribution. ### In Telecommunications and Networking: 1. **Telecommunications**: A feeder line may connect a central office or a hub to a distribution point or remote terminal.
Radia Perlman is an American computer scientist and network engineer, known for her pioneering work in the field of computer networking. She is most famous for her invention of the Spanning Tree Protocol (STP), which is critical for the operation of Ethernet networks. STP helps prevent loops in network topologies by allowing switches to communicate and design efficient data paths. Perlman has contributed significantly to various areas in networking, including secure routing, network protocols, and network security.
In mathematics, particularly in the context of topology and algebraic geometry, a **K-cell** typically refers to a specific type of structure used in the study of cellular complexes. K-cells are often used in the construction and analysis of CW complexes, which are certain types of topological spaces. A K-cell generally consists of two components: 1. **A dimension**: The "K" in K-cell usually denotes its dimension.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.Figure 4. Visual Studio Code extension tree navigation.Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact





