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

Chu Space

... space by dropping the requirements that the

... 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

... 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

... 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

... 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

... 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)

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