In topology, a **uniformizable space** is a type of topological space that can be equipped with a uniform structure. A uniform structure provides a way to formalize notions of uniform continuity and convergence, which extend the idea of uniformity that one might encounter in metric spaces. ### Definitions 1.
Point-to-point (P2P) telecommunications refer to a direct connection established between two communication endpoints or nodes. This setup allows for a dedicated communication link, which can be used for various forms of data transmission, including voice, video, and data signals. Point-to-point connections are typically contrasted with point-to-multipoint setups, where one node communicates with multiple endpoints.
Albert Schwarz is a renowned mathematician known for his contributions to various fields, particularly in topology and geometry. He is noted for the Schwarz lemma and is often referenced in discussions related to complex analysis and differential geometry.
Benson Farb is a mathematician known for his work in topology and geometry, particularly in the areas of algebraic topology and the study of mapping class groups. He has contributed significantly to the understanding of the properties of surfaces and their symmetries, as well as the mathematical structures that arise from these studies. Farb is also involved in mathematical outreach and education, and he has authored or co-authored several research papers and books in his field.
Colin Adams is a mathematician known for his work in the field of topology, particularly in low-dimensional topology and knot theory. He is a professor at Williams College in Massachusetts and has contributed significantly to the understanding of knots and 3-manifolds. Adams is also noted for his ability to communicate mathematical concepts to a broader audience, often engaging in outreach and popular mathematics.
Richard Lashof is an American scientist and professor known for his work in the field of environmental science, particularly focusing on the impacts of climate change and air quality. He has been involved with various organizations and initiatives aimed at addressing issues related to environmental sustainability and public health.
In category theory and algebraic topology, the concept of *fibration* is a generalization of the notion of a fiber bundle. When we speak of a fibration of simplicial sets, we are referring to a specific type of fibration within the context of simplicial sets, which serve as a combinatorial model for topological spaces. ### Simplicial Sets A **simplicial set** is a combinatorial structure that encodes information about topological spaces.
Alfred North Whitehead was an English mathematician and philosopher known for his work in various fields, including philosophy of science, metaphysics, logic, and education. His major works reflect his systematic approach to philosophy and his interest in process and change. Here are some of his most notable works: 1. **"Principia Mathematica" (1910-1913)** - Co-authored with Bertrand Russell, this monumental work aimed to establish a solid foundation for mathematics using formal logic.
Bertrand Russell (1872–1970) was a British philosopher, logician, mathematician, historian, and social critic. He is best known for his work in mathematical logic and analytical philosophy, making significant contributions to a wide range of fields, including philosophy of language, epistemology, ethics, and political theory. Russell was a prominent figure in the development of modern logic and is one of the founders of analytic philosophy, along with figures like G.E.
A Pure Type System (PTS) is a type-theoretical framework used in computer science and mathematical logic for defining and analyzing programming languages. It generalizes certain typing systems, allowing for the expression of a wide variety of type theories and their associated computational behaviors. Here are some key aspects of Pure Type Systems: 1. **Basic Structure**: A PTS consists of a set of types and terms, along with rules for how types can be constructed from each other and how terms can be typed.
Étienne-Gabriel Morelly (also spelled Morelly) was an 18th-century French philosopher and writer, known primarily for his work in social and political philosophy. He is often associated with early socialist thought and is best known for his book "Code de la nature" (Code of Nature), published in 1755.
Skills-based routing is a strategy used in customer service and contact center environments to match incoming inquiries or requests to the most qualified agent or representative based on their specific skills and expertise. This approach ensures that customers receive assistance from agents who are best equipped to address their needs efficiently. ### Key Components of Skills-Based Routing: 1. **Skill Identification**: Agents are assigned specific skills or competencies based on their training, experience, and areas of expertise.
The Rydberg constant is a fundamental physical constant that characterizes the wavelengths of spectral lines in many chemical elements, particularly hydrogen. It is named after the Swedish physicist Johannes Rydberg, who formulated a formula in the 1880s to predict the wavelengths of the spectral lines of hydrogen.
The "blue hour" refers to the period of twilight after sunset or before sunrise when the sky takes on a deep blue hue. This phenomenon occurs when the sun is below the horizon but still illuminates the atmosphere, scattering the shorter wavelengths of light. The blue hour is particularly favored by photographers and artists because of the soft, diffused light it creates, which can enhance the mood and color of the landscape.
Room 641A is a secure telecommunications interception facility operated by the National Security Agency (NSA) in the United States. It is part of the NSA's broader surveillance efforts, and it reportedly contains equipment designed to monitor and analyze electronic communications, including phone calls and internet traffic.
Specific activity is a term commonly used in biochemistry and molecular biology to refer to the activity of an enzyme, protein, or other biological molecule per unit of mass or concentration. It is typically expressed as units of enzyme activity (such as micromoles of substrate converted per minute) per milligram of protein, or in a similar measurement that allows comparison of the activity relative to the amount of the substance present.
The New Zealand Map Grid (NZMG) is a geodetic coordinate system used for mapping and surveying purposes in New Zealand. It provides a uniform framework for locating features on the Earth's surface within the country. The NZMG is based on the Transverse Mercator projection and was established to enable accurate and consistent mapping across New Zealand.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . 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. - 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