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sparables

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Definitions of sparables in various dictionaries:

noun - a type of nail

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Sparables might refer to
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence * * * * { * * x * * n * * * * } * * n * = * 1 * * * ∞ * * * * * {\displaystyle \{x_{n}\}_{n=1}^{\infty }} * of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence. * Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense. In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset. * Contrast separability with the related notion of second countability, which is in general stronger but equivalent on the class of metrizable spaces.

Sparables might refer to

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence
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* {\displaystyle \{x_{n}\}_{n=1}^{\infty }}
* of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
* Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense. In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset.
* Contrast separability with the related notion of second countability, which is in general stronger but equivalent on the class of metrizable spaces.

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