Connected spaceIn topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space is a if it is a connected space when viewed as a subspace of . Some related but stronger conditions are path connected, simply connected, and -connected.
Locally connected spaceIn topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets. Throughout the history of topology, connectedness and compactness have been two of the most widely studied topological properties. Indeed, the study of these properties even among subsets of Euclidean space, and the recognition of their independence from the particular form of the Euclidean metric, played a large role in clarifying the notion of a topological property and thus a topological space.
Moyal bracketIn physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product. The Moyal bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a lengthy dispute with Paul Dirac. In the meantime this idea was independently introduced in 1946 by Hip Groenewold. The Moyal bracket is a way of describing the commutator of observables in the phase space formulation of quantum mechanics when these observables are described as functions on phase space.
Partition typeThe partition type (or partition ID) in a partition's entry in the partition table inside a master boot record (MBR) is a byte value intended to specify the the partition contains or to flag special access methods used to access these partitions (e.g. special CHS mappings, LBA access, logical mapped geometries, special driver access, hidden partitions, secured or encrypted file systems, etc.). Lists of assigned partition types to be used in the partition table in the MBR were originally maintained by IBM and Microsoft internally.
SphereA sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry.
Covering spaceA covering of a topological space is a continuous map with special properties. Let be a topological space. A covering of is a continuous map such that there exists a discrete space and for every an open neighborhood , such that and is a homeomorphism for every . Often, the notion of a covering is used for the covering space as well as for the map . The open sets are called sheets, which are uniquely determined up to a homeomorphism if is connected. For each the discrete subset is called the fiber of .
Master boot recordA master boot record (MBR) is a special type of boot sector at the very beginning of partitioned computer mass storage devices like fixed disks or removable drives intended for use with IBM PC-compatible systems and beyond. The concept of MBRs was publicly introduced in 1983 with PC DOS 2.0. The MBR holds the information on how the disc's sectors (aka “blocks”) are divided into partitions, each partition notionally containing a file system.
Extended boot recordAn extended boot record (EBR), or extended partition boot record (EPBR), is a descriptor for a logical partition under the common DOS disk drive partitioning system. In that system, when one (and only one) partition record entry in the master boot record (MBR) is designated an extended partition, then that partition can be subdivided into a number of logical partitions. The actual structure of that extended partition is described by one or more EBRs, which are located inside the extended partition.
Surface energyIn surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material (the atoms on the surface have more energy compared with the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see sublimation).
Volume boot recordA volume boot record (VBR) (also known as a volume boot sector, a partition boot record or a partition boot sector) is a type of boot sector introduced by the IBM Personal Computer. It may be found on a partitioned data storage device, such as a hard disk, or an unpartitioned device, such as a floppy disk, and contains machine code for bootstrapping programs (usually, but not necessarily, operating systems) stored in other parts of the device. On non-partitioned storage devices, it is the first sector of the device.
Covering groupIn mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups.
Branched coveringIn mathematics, a branched covering is a map that is almost a covering map, except on a small set. In topology, a map is a branched covering if it is a covering map everywhere except for a nowhere dense set known as the branch set. Examples include the map from a wedge of circles to a single circle, where the map is a homeomorphism on each circle. In algebraic geometry, the term branched covering is used to describe morphisms from an algebraic variety to another one , the two dimensions being the same, and the typical fibre of being of dimension 0.
