This page explains commonly used terms in chess in alphabetical order. Some of these have their own pages, like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of chess-related games, see Chess variants.

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

[adjective: prophylactic] Prophylactic techniques include the blockade, overprotection, and the mysterious rook move.

Q

R

S

T

U

V

W

X

Z

References

Bibliography

In mathematics, a space is a set (sometimes called a universe) with some added structure.

Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space. For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space such that:

where the norm is indicated by enclosing in double vertical lines, and the inner product is indicated enclosing in by angle brackets.

Modern mathematics treats "space" quite differently compared to classical mathematics.

History

Before the golden age of geometry

In the ancient mathematics, "space" was a geometric abstraction of the three-dimensional space observed in the everyday life. Axiomatic method had been the main research tool since Euclid (about 300 BC). The method of coordinates (analytic geometry) was adopted by René Descartes in 1637. At that time, geometric theorems were treated as an absolute objective truth knowable through intuition and reason, similar to objects of natural science; and axioms were treated as obvious implications of definitions.

A five-dimensional space is a space with five dimensions. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativitistic physics. It is an abstraction which occurs frequently in mathematics, where it is a legitimate construct. In physics and mathematics, a sequence of N numbers can be understood to represent a location in an N-dimensional space. Whether or not the actual universe in which we live is five-dimensional is a topic of debate.

Physics

Much of the early work on five dimensional space was in an attempt to develop a theory that unifies the four fundamental forces in nature: strong and weak nuclear forces, gravity and electromagnetism. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.

Universe: The Definitive Visual Guide is a 528-page, non-fiction book by nine British co-authors (listed alphabetically below) with a short Foreword by Sir Martin Rees, first published in 2005. The book is divided into three sections, beginning with an introduction to theories of the Universe, space exploration, Earth's view of space and how the Universe will end. The second section, "Guide to the Universe," contains information on the Sun and the Solar System, as well as the Milky Way and other types of galaxies. The last section, "The Night Sky," has full-page maps and charts of the night sky for both northern and southern viewers as well as a comprehensive list of the constellations. The book contains full-colour pictures, maps, and probe photographs. There are in-depth looks at features of planets in the Solar System, such as Venus's craters and Mars's ridges. There are also captions describing the scientists and stories behind various discoveries. The book was produced in London, England, by Dorling Kindersley and is published internationally. A revised and updated edition was published in September 2007, including recent developments such as the reclassification of Pluto as a dwarf planet. In October 2012, the book was revised for a third time adding newly discovered information about planets in other planetary systems and water on Mars.

In mathematics, and particularly in set theory and the foundations of mathematics, a universe is a class that contains (as elements) all the entities one wishes to consider in a given situation. There are several versions of this general idea, described in the following sections.

In a specific context

Perhaps the simplest version is that any set can be a universe, so long as the object of study is confined to that particular set. If the object of study is formed by the real numbers, then the real line R, which is the real number set, could be the universe under consideration. Implicitly, this is the universe that Georg Cantor was using when he first developed modern naive set theory and cardinality in the 1870s and 1880s in applications to real analysis. The only sets that Cantor was originally interested in were subsets of R.

This concept of a universe is reflected in the use of Venn diagrams. In a Venn diagram, the action traditionally takes place inside a large rectangle that represents the universe U. One generally says that sets are represented by circles; but these sets can only be subsets of U. The complement of a set A is then given by that portion of the rectangle outside of A's circle. Strictly speaking, this is the relative complement U \ A of A relative to U; but in a context where U is the universe, it can be regarded as the absolute complement A^C of A. Similarly, there is a notion of the nullary intersection, that is the intersection of zero sets (meaning no sets, not null sets). Without a universe, the nullary intersection would be the set of absolutely everything, which is generally regarded as impossible; but with the universe in mind, the nullary intersection can be treated as the set of everything under consideration, which is simply U.

Rocket U2 is a suite of database management (DBMS) and supporting software now owned by Rocket Software. It includes two MultiValue database platforms: UniData and UniVerse. Both of these products are operating environments which run on current Unix, Linux and Windows operating systems. They are both derivatives of the Pick operating system. The family also includes developer and web-enabling technologies including SystemBuilder/SB+, SB/XA, U2 Web Development Environment (WebDE), UniObjects and wIntegrate.

History

UniVerse was originally developed by VMark Software and UniData was originally developed by the Unidata Corporation. Both Universe and Unidata are used for vertical application development and are embedded into the vertical software applications. In 1997, the Unidata Corporation merged with VMark Systems to form Ardent Software. In March 2000, Ardent Software was acquired by Informix. IBM subsequently acquired the database division of Informix in April 2001, making UniVerse and UniData part of IBM's DB2 product family. IBM subsequently created the Information Management group of which Data Management is one of the sub-areas under which the IBM U2 family comprised UniData and UniVerse along with the tools, SystemBuilder Extensible Architecture (SB/XA), U2 Web Development Environment (U2 Web DE) and wIntegrate.

Andre DiJuan Daniels (born March 31, 1986), better known by his stage name Add-2, sometimes stylized as Add 2, is an American rapper from Chicago, Illinois. He first gained popularity after the release of his second mixtape, A Tale of Two's City: Volume 2. In 2009, his single "Luxury" was featured on MTV,MtvU's top 5 freshman and Vh1 respectively. "Luxury" is part of Add-2's third mixtape, "Tale of Two's City Vol. 3: The Rise & Fall." Add-2 has also worked with Grammy award winning music producer 9th Wonder along with Kendrick Lamar,The Roots and Gerald Walker.

Discography

Guest Appearances