The term "size homotopy group" does not appear to be a standard term in algebraic topology or related fields as of my last knowledge update in October 2023.

A simplicial set is a fundamental concept in algebraic topology and category theory that generalizes the notion of a topological space. It is a combinatorial structure used to study objects in homotopy theory and other areas of mathematics. ### Definition A **simplicial set** consists of: 1. **Sets of n-simplices**: For each non-negative integer \( n \), there is a set \( S_n \) which consists of n-simplices.

Semi-s-cobordism is a concept in the field of algebraic topology, particularly in the study of manifolds and cobordism theory. It can be considered a refinement of the notion of cobordism, which is related to the idea of two manifolds being "compatible" in terms of their boundaries.

A Surgery Structure Set typically refers to a collection of specific anatomical structures and their corresponding definitions used in surgical planning, especially in the context of medical imaging and surgical procedures. In disciplines like radiology and radiation oncology, a structure set is a set of delineated areas on medical images (such as CT or MRI scans) that represent various organs, tissues, or pathological areas relevant for treatment.

In topology, "tautness" refers to a property of a mapping between two topological spaces, specifically in the context of a topological space being a **taut space**. A topological space is characterized as a taut space if it has certain conditions related to continuous mappings, particularly concerning their compactness and how they relate to other properties like being perfect, locally compact, or having specific kinds of bases.

The Whitehead conjecture is a statement in the field of topology, particularly concerning the structure of certain types of topological spaces and groups. It posits that if a certain type of group, specifically a finitely generated group, has a particular kind of embedding in a higher-dimensional space, then this embedding can be lifted to a map from a higher-dimensional space itself.

The Vietoris-Rips complex is a construction used in algebraic topology and specifically in the study of topological spaces through point cloud data. It offers a way to build a simplicial complex from a discrete set of points, often used in the field of topological data analysis (TDA).

Volodin space, often denoted as \( V_0 \), is a type of function space that arises in the context of functional analysis and distribution theory. It is primarily used in the study of linear partial differential equations and the theory of distributions (generalized functions). Specifically, Volodin spaces consist of smooth functions (infinitely differentiable functions) that behave well under certain linear differential operators.

Abu Kamil, also known as Abu Kamil Shuja ibn Aslam, was a notable mathematician from the Abbasid period, specifically around the 9th to 10th centuries. He is often recognized as a significant figure in the development of algebra. His work built upon that of earlier mathematicians, including Al-Khwarizmi, and contributed to the transmission of mathematical knowledge from the Islamic world to Europe.

Ernst Witt (1911–1991) was a prominent German mathematician known primarily for his work in algebra and group theory. He made significant contributions to the study of algebraic groups and related areas. Witt is perhaps best known for the development of the "Witt decomposition," which provides a way to decompose certain bilinear forms, and the "Witt hypothesis," related to the structure of certain types of algebraic groups.

In algebraic geometry, the term "pseudo-canonical variety" often refers to a type of algebraic variety whose canonical class behaves in a particular way. While the term itself may not be universally defined in all texts, it is sometimes used in the context of the study of varieties with singularities, particularly in relation to the minimal model program (MMP) and the study of Fano varieties.

Alexander Grothendieck (1928–2014) was a highly influential French mathematician, renowned for his groundbreaking work in algebraic geometry, homological algebra, and number theory. He is often considered one of the most important mathematicians of the 20th century. Grothendieck's contributions include the development of a new way of thinking about algebraic geometry through the use of schemes, a concept that generalized classical algebraic varieties.

Bill Casselman is a mathematician known for his work in the field of mathematics, particularly in analysis and number theory. He has made significant contributions to mathematical education and has created a variety of online resources, including mathematical puzzles and explanations. He has a popular website featuring mathematical problems, discussions, and insights aimed at both students and educators. Additionally, Casselman was involved in developing mathematical software and has published academic papers.

Carolyn Yackel is a mathematician known for her work in the field of mathematics education, particularly in the areas of topology and mathematics communication. She has made significant contributions to the outreach and promotion of mathematical learning and understanding. Yackel is also known for her research in mathematics education, exploring how people learn math and how teaching practices can be improved.

Bartel Leendert van der Waerden (1903–1996) was a prominent Dutch mathematician known for his work in abstract algebra, particularly in the areas of algebraic notation, number theory, and combinatorics. He is perhaps best known for van der Waerden's theorem in combinatorics, which concerns the existence of certain arithmetic progressions in sets of natural numbers.

Colin McLarty is a mathematician known for his work in the philosophy of mathematics and mathematical logic. He is particularly recognized for his contributions to the foundations of mathematics and the connections between mathematical practice and philosophical inquiry. McLarty has written extensively on topics such as the role of diagrams in mathematics, the nature of mathematical proof, and the interpretation of mathematical theories.

Douglas Northcott is best known as a British former child actor who gained fame in the late 1950s and 1960s. He starred in films and television series during that time, often recognized for his performances in roles that showcased his talent at a young age. However, he is not as widely known in contemporary discussions, and information about his later life or career might be limited.

Erland Samuel Bring (1735–1798) was a Swedish mathematician and astronomer known for his contributions to various fields, including mathematics, physics, and mechanics. He is particularly noted for his work on mathematical analysis and differential equations. Bring is recognized for his involvement in the development of mathematical concepts that are foundational to modern mathematics. One of his notable contributions is the "Bring radical," which is associated with solving certain polynomial equations.

Eugene Dynkin is a notable mathematician recognized for his contributions to various fields, particularly in probability theory, stochastic processes, and mathematical finance. He is renowned for the development of Dynkin's theorem, which connects martingales (a type of stochastic process) with time-homogeneous Markov processes. Dynkin has also contributed to the study of Dynkin games, which are a type of strategic game theory problem that involves players making decisions over time under uncertainty.

François Viète (also known as Francis Vieta) was a French mathematician born on February 5, 1540, and died on February 23, 1603. He is best known for his contributions to algebra, particularly for developing a systematic approach to the application of algebraic methods to geometry, and for introducing new notations that significantly advanced mathematical thinking.