A metric map is a mathematical concept used in various fields such as geometry, topology, and data analysis. It typically refers to a function between two metric spaces that preserves certain properties related to distances. Here’s a brief overview: 1. **Metric Space**: A metric space is a set equipped with a distance function (or metric) that defines the distance between any two points in the set.

In the context of topology and metric spaces, a **metric space** is a set \( X \) along with a metric \( d \) that defines a distance between any two points in \( X \). A **subspace** of a metric space is essentially a subset of that metric space that inherits the structure of the original space. ### Definition of Metric Space A metric space \( (X, d) \) consists of: - A set \( X \).

In the context of topology and set theory, particularly in metric spaces, "positively separated sets" refers to a specific condition regarding the distance between two sets.

In topology, a space is termed "uniformly disconnected" if it satisfies a particular property related to the concept of uniformity in topology. A uniformly disconnected space is a type of topological space in which disjoint open sets can be separated in a uniform manner across the entire space. More formally, a topological space \( X \) is called uniformly disconnected if every continuous function from \( X \) into a compact Hausdorff space is uniformly continuous.

Bent's rule is a principle in chemistry that pertains to the hybridization of atomic orbitals in heteroatomic molecules, particularly those containing a central atom bonded to different substituents. Formulated by Linus Pauling and named after the chemist Robert S. Bent, the rule states that: "In a molecule, the more electronegative atoms will tend to occupy positions that allow for greater p-character in the hybrid orbitals formed by the central atom.

The Berry mechanism, also known as the Berry phase or Berry's phase, is a fundamental concept in quantum mechanics and condensed matter physics. It describes a geometric phase acquired by the quantum state of a system when the system is subject to adiabatic (slow) changes in its parameters. The core idea is that when a quantum system is driven around a closed loop in parameter space, its wave function can acquire a phase factor that is not attributed to the dynamics of the system itself (i.e.

Capped octahedral molecular geometry refers to a specific arrangement of atoms in a molecule where an octahedral structure is complemented by additional atoms or groups that occupy positions above or below the octahedron. In an octahedral geometry, the central atom is surrounded by six other atoms at the corners of a regular octahedron. In capped octahedral geometry, there are typically two additional atoms or groups that "cap" the top and bottom faces of the octahedron.

A diatomic molecule is a molecule that consists of two atoms. These atoms can be of the same element or of different elements. Diatomic molecules can be found in various forms, including: 1. **Homodiatomic molecules**: These consist of two atoms of the same element. Examples include: - Oxygen (O₂) - Nitrogen (N₂) - Hydrogen (H₂) - Chlorine (Cl₂) 2.

Hypercubane is a theoretical carbon allotrope that is a polyhedral structure made up of interconnected carbon atoms arranged in a fashion analogous to a hypercube or tesseract in higher dimensions. The name "hypercubane" combines "hypercube" and "cubane," a well-known hydrocarbon with a cubic structure where carbon atoms form the vertices of a cube.

An open-chain compound, also known as a linear compound, is a type of chemical compound characterized by a straight or branched chain of atoms, typically consisting of carbon (C) and hydrogen (H) atoms. In open-chain compounds, the atoms are connected by single, double, or triple bonds, but there are no closed rings or cyclic structures.

The term "end group" can refer to different concepts depending on the context in which it is used. Here are a few common interpretations: 1. **Chemistry/Polymer Science**: In polymer chemistry, end groups are the functional groups or atoms that are located at the ends of a polymer chain. These groups play a crucial role in defining the properties of the polymer, as they can influence reactivity, solubility, and other physical characteristics.

Pentagonal bipyramidal molecular geometry is a type of molecular structure that occurs when a central atom is surrounded by 7 other atoms positioned at the vertices of a geometry resembling two pyramids (bipyramids) sharing a common base. In this geometry, the central atom typically exhibits an coordination number of 7.

A triangular bipyramid is a type of polyhedron that consists of two pyramids base-to-base, with a triangular base. It has a total of five faces, nine edges, and six vertices. ### Properties of a Triangular Bipyramid: 1. **Faces**: It has five faces, which include: - 2 triangular faces from the pyramids at the top and bottom. - 3 triangular faces that connect the vertices of the triangular bases.

Aslı Erdoğan is a Turkish author, writer, and human rights advocate, known for her literature that often explores themes of identity, exile, and the struggles faced by marginalized communities. Born on March 20, 1967, in Istanbul, Erdoğan has written novels, essays, and short stories that have garnered critical acclaim both in Turkey and internationally. Her literary works include titles such as "The City in the Black" and "The Stone Building and Other Places.

Trigonal prismatic molecular geometry is a type of molecular structure where a central atom is surrounded by six other atoms arranged at the corners of a prism with a triangular base. This geometry is characterized by having two triangular faces and three rectangular faces, similar to a prism shape.

VSEPR theory, or Valence Shell Electron Pair Repulsion theory, is a model used in chemistry to predict the three-dimensional shapes of molecules based on the repulsion between electron pairs in the valence shell of atoms. The fundamental concept behind VSEPR theory is that electron pairs, whether they are bonding pairs (shared between atoms) or lone pairs (non-bonding electrons that belong to a single atom), repel each other due to their negative charge.

In chemistry, the term "vicinal" typically refers to two functional groups or substituents that are located on adjacent carbon atoms in a molecule. The term is often used in the context of vicinal diols, where two hydroxyl (-OH) groups are attached to two adjacent carbon atoms.

Behram Kurşunoğlu was a prominent Turkish physicist known for his work in theoretical physics, particularly in areas such as quantum mechanics and mathematical physics. He made significant contributions to various scientific fields and is recognized for his research and academic work. Kurşunoğlu was also involved in education and mentoring students in physics.

Hakkı Ögelman is a name that may refer to a specific individual, typically recognized within certain contexts, possibly in Turkey or among Turkish-speaking communities. However, without additional context or details, it's challenging to provide specific information.

İsmail Hakkı Duru is a Turkish name, but there is limited publicly available information about a notable individual by that name. It is possible that he could be a private individual, a local figure, or someone not widely recognized in major media or academic sources.