Sequence space

In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space.

The most important sequences spaces in analysis are the ℓ^p spaces, consisting of the p-power summable sequences, with the p-norm. These are special cases of L^p spaces for the counting measure on the set of natural numbers. Other important classes of sequences like convergent sequences or null sequences form sequence spaces, respectively denoted c and c₀, with the sup norm. Any sequence space can also be equipped with the topology of pointwise convergence, under which it becomes a special kind of Fréchet space called FK-space.

Space

Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

Glossary of chess

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.

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

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References

Bibliography

Space (The Arrogant Worms album)

Space, stylized as SPACE, is the fourteenth album by the Canadian comedy music group, The Arrogant Worms. It was released in March 2014.

Track listing