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Definition: "Areolated" is a term used in mathematics to describe a set or object that is not connected to any other objects. It can be defined as "a subset of a given set that does not contain any elements that are also members of the set." This concept is often used in topology and algebra, where it refers to isolated points or subspaces.
Definition: Avigation is a term used in mathematics to describe an object or process that involves moving along a path. It can refer to a series of steps, a sequence of events, or a journey through space. In mathematical terms, it could be defined as "an operation on a set X" where the goal is to find all the subsets of X that satisfy certain conditions. For example, in the context of algebraic geometry, an avigation problem might involve finding all the subspaces of a vector
Definition: In mathematics, "supercanonical" refers to a specific type of configuration space in geometric topology. Supercanonically defined spaces are those for which all but one point is non-orientable. The concept of supercanonically defined spaces was introduced by John Nash and others in the 1970s. It involves a topological space X with a collection of subspaces, called the canonical subspaces, that define its fundamental group π_1(X). These subspaces are required
Definition: In mathematics, a subspace is a subset of a larger space that contains all its own elements but excludes any others. Subspaces are fundamental in linear algebra and provide a way to partition spaces into simpler geometric entities.
Definition: In mathematics, a subdivecious set is defined as a subset of a vector space that contains one or more vectors which are linearly independent. Subdivecious sets are important for understanding and working with subspaces in linear algebra. A subdivecious set can be constructed by adding additional basis vectors to the original space. For example, if we have a 3-dimensional vector space V over a field F, and we want to construct a subspace H containing the zero vector (
Definition: In mathematics, a nonlocally defined space (also known as an uncountable locally countably infinite space) is a topological space that has no finite subspaces. That means it can be represented by a union of countably many open sets without any choice. For example: 1. The real line $\mathbb{R}$ is nonlocally defined because there are infinitely many open intervals in the plane $(0, 1)$. 2. The complex numbers $\mathbb{
Definition: In mathematics, a non-vacuum set is a subset of an infinite-dimensional vector space that has no finite subspaces or linear combinations that are either equal to zero or orthogonal. This concept is fundamental in many areas of mathematics and physics, particularly in studying manifolds with boundary and their associated Lie groups.
Definition: In mathematics, a midline is a line that divides a curve into two equal parts. It's often used in geometry and algebra to represent lines or planes. For example, if you have a graph where the x-axis represents the position of an object as it moves from left to right, then the y-axis would be its height, which is represented by the midline. In linear algebra, a midline is a line through the origin that divides a vector space into two subspaces. It
Definition: Lattice is a mathematical concept in the field of algebraic geometry, specifically in the context of projective varieties. It refers to a set of points that are coplanar but not necessarily tangent to each other. In other words, it represents the intersection of two surfaces (or higher-dimensional objects) in such a way that they do not touch or intersect at all. The term "lattice" comes from the fact that these sets can be used as subspaces in a vector space over a
Definition: The term "lagend" is a term used in the field of mathematics, specifically in linear algebra. It refers to a vector space that has zero-dimensional subspaces. In other words, if V is a vector space over a field K and L is a subspace of V, then L is called a zero-dimensional subspace of V if there exists a basis B of V such that the span of vectors in B forms an empty set (i.e., it has no elements).