Open Sets

Some articles on set, open sets, open, open set:

Chu Space
... space by dropping the requirements that the set of open sets be closed under union and finite intersection, that the open sets be extensional, and that the ...
Borel Hierarchy - Lightface Hierarchy
... It is important in effective descriptive set theory and recursion theory ... and codes for elements of the classes, are inductively defined as follows A set is if and only if it is effectively open, that is, an open set which is the union of a computably enumerable sequence of basic open ... A code for such a set is a pair (0,e), where e is the index of a program enumerating the sequence of basic open sets ...
Curtis–Hedlund–Lyndon Theorem - Definitions
... An alphabet is any finite set of symbols, which may be thought of as the states of the cells in a cellular automaton ... A pattern is a finite set of positions and an assignment of symbols to each of these positions ... The shift space is the set of all possible configurations over a given alphabet ...
Fürstenberg's Proof Of The Infinitude Of Primes - Furstenberg's Proof
... integer topology, by declaring a subset U ⊆ Z to be an open set if and only if it is either the empty set, ∅, or it is a union of arithmetic sequences S(a, b) (for a ≠ 0), where In other words ... The axioms for a topology are easily verified By definition, ∅ is open Z is just the sequence S(1, 0), and so is open as well ... Any union of open sets is open for any collection of open sets Ui and x in their union U, any of the numbers ai for which S(ai, x) ⊆ Ui also shows that S(ai, x) ⊆ U ...
Borel Determinacy Theorem - Background - Topology
... For a given set A, whether a subset of Aω will be determined depends to some extent on its topological structure ... purposes of Gale–Stewart games, the set A is endowed with the discrete topology, and Aω endowed with the resulting product topology, where Aω is viewed as a countably ... In particular, when A is the set {0,1}, the topology defined on Aω is exactly the ordinary topology on Cantor space, and when A is the set of ...

Famous quotes containing the words sets and/or open:

    A horse, a buggy and several sets of harness, valued in all at about $250, were stolen last night from the stable of Howard Quinlan, near Kingsville. The county police are at work on the case, but so far no trace of either thieves or booty has been found.
    —H.L. (Henry Lewis)

    It is an open question whether any behavior based on fear of eternal punishment can be regarded as ethical or should be regarded as merely cowardly.
    Margaret Mead (1901–1978)