basic open setの例文

• The basic open sets of the product topology are cylinder sets, here characterized as:
• The open sets of " A " ? are precisely the sets expressible as unions of these basic open sets.
• Every metric space can be given a metric topology, in which the basic open sets are open balls defined by the metric.
• Each sequence in the bar represents a basic open set of this space, and these basic open sets cover the space by assumption.
• Each sequence in the bar represents a basic open set of this space, and these basic open sets cover the space by assumption.
• Thus a basic open set in the Baire space is the set of all infinite sequences of natural numbers extending a common finite initial segment & tau;.
• Basic open sets in the discrete topology consist of individual letters; thus, the open cylinders of the product topology on S ^ \ mathbb { Z } are
• The " N " of the fan theorem can be taken to be the length of the longest sequence whose basic open set is in the finite subcover.
• The set " A " & omega; can be viewed as the set of paths through a certain basic open set in the topology on " A ".
• Similarly, an index for a \ Pi ^ 0 _ 1 set " B " describes the computable function enumerating the basic open sets in the complement of " B ".
• Thus each \ Sigma ^ 0 _ 1 set has at least one "'index "', which describes the computable function enumerating the basic open sets from which it is composed; in fact it will have infinitely many such indices.