BC Brno is a basketball club based in Brno, Czech Republic. The team has a history of participating in various international competitions, including tournaments such as the FIBA EuroCup, the Champions League, and others that include clubs from across Europe. BC Brno has a notable presence in the Czech basketball league and has been competitive on the international stage as well. The club's involvement in these competitions provides opportunities for showcasing talent and gaining experience against a variety of teams from different countries.

Diastole is the phase of the cardiac cycle during which the heart muscle relaxes and the chambers of the heart fill with blood. It occurs after systole, which is the phase when the heart muscles contract to pump blood out of the heart. Diastole is crucial for ensuring that the heart has enough blood to pump out during the next contraction.

Probabilistic causation refers to the conceptual framework in which causation is understood in probabilistic rather than deterministic terms. In traditional deterministic causation, an event (the cause) leads to a specific outcome (the effect) with certainty. However, in many real-world scenarios, causes do not guarantee a specific effect but rather influence the likelihood or probability of that effect occurring.

A Heyting algebra is a specific type of mathematical structure that arises in the field of lattice theory and intuitionistic logic. Heyting algebras generalize Boolean algebras, which are used in classical logic, by accommodating the principles of intuitionistic logic. ### Definition A Heyting algebra is a bounded lattice \( H \) equipped with an implication operation \( \to \) that satisfies certain conditions.

Algebraic cobordism is a cohomology theory in algebraic geometry that emerges from the study of algebraic cycles and their intersections. It provides a space to study algebraic varieties in a manner similar to how bordism theories function in topology. The notion of cobordism in algebraic geometry can be understood as a way to classify algebraic varieties (or schemes) through the idea of "cobordism classes" that respect certain algebraic operations and relations.

In the context of graph theory and topology, a **clique complex** is a type of simplicial complex that is constructed from the cliques of a graph. A clique, in graph terminology, refers to a subset of vertices that are all adjacent to each other, meaning there is an edge between every pair of vertices in that subset.

A combinatorial map is a mathematical structure used primarily in the field of topology and combinatorial geometry. It provides a way to represent and manipulate geometrical objects, particularly in the context of surfaces and subdivision of spaces. The main features of a combinatorial map include: 1. **Vertex-Edge-Face Representation**: Combinatorial maps describe the relationships between vertices (0-dimension), edges (1-dimension), and faces (2-dimension).

In topology, the **cone** is a fundamental construction that captures the idea of collapsing a space into a single point. Specifically, the cone over a topological space \( X \) is denoted as \( \text{Cone}(X) \) and can be described intuitively as "taking the space \( X \) and stretching it up to a point.

A duocylinder is a geometric shape that can be described as the three-dimensional analogue of a two-dimensional rectangle, specifically in the context of higher-dimensional geometry. More formally, a duocylinder is the Cartesian product of two cylinders, which means it is the result of taking two cylinders and combining their dimensions.

Fiber-homotopy equivalence is a concept in the field of algebraic topology, specifically in the study of fiber bundles and homotopy theory. In general, it pertains to a relationship between two fiber bundles that preserves the homotopy type of the fibers over the base space.

In algebraic geometry and topology, a **sheaf of spectra** is typically a construction involving the **spectrum** of a commutative ring or a more general algebraic structure. To understand this concept, we first need to clarify some terms: 1. **Spectrum of a ring**: The spectrum of a commutative ring \( R \), denoted as \( \text{Spec}(R) \), is the set of prime ideals of \( R \).

In the context of mathematics, particularly in algebraic topology, the **fundamental class** refers to a specific object associated with a homology class of a manifold or a topological space. It is particularly significant in the study of dimensional homology. Here's a more detailed explanation: 1. **Homology Theory**: Homology is a mathematical concept used to study topological spaces through algebraic invariants. It provides a way to classify spaces based on their shapes and features like holes.

The Redshift conjecture is a hypothesis in the field of astrophysics, particularly related to the study of galaxies and cosmic structures. The conjecture posits that the observed redshift of galaxies is primarily due to the expansion of the universe rather than a simple Doppler effect from motion through space. In essence, it suggests that the redshift is linked to the fabric of spacetime expanding, which stretches the light waves traveling through it, leading to an increase in their wavelength (redshift).

In category theory, the **size functor** is a concept that relates to the notion of the "size" or "cardinality" of objects in a category. While the term "size functor" may not be universally defined in all contexts, it often appears in discussions concerning the sizes of sets or types in the context of type theory, category theory, and functional programming.

A spinor bundle is a specific type of vector bundle that arises in the context of differential geometry and the theory of spinors, particularly in relation to Riemannian and pseudo-Riemannian manifolds. Here’s a more in-depth explanation: ### Context In the study of geometrical structures on manifolds, one often encounters vector bundles, which are collections of vector spaces parameterized by the points of a manifold.

Topological modular forms (TMF) are a sophisticated concept in the fields of algebraic topology and homotopy theory that serves as a bridge between various areas of mathematics, including topology, number theory, and algebraic geometry. They can be understood as a generalization of modular forms, which are complex analytic functions with specific transformation properties and play a central role in number theory.

In the context of topology, a "topological pair" typically refers to a pair consisting of a topological space and a subset of that space, often denoted as \((X, A)\), where \(X\) is a topological space and \(A\) is a subset of \(X\). This concept is particularly useful in algebraic topology and can be used to study various properties of spaces and the relationship between spaces and their subspaces.

Additive categories are a specific type of category in the field of category theory, which is a branch of mathematics that deals with abstract structures and relationships between them. An additive category can be thought of as a category that has some additional structure that makes it behave somewhat like the category of abelian groups or vector spaces.