separable space

(redirected from Separable metric space)

separable space

[′sep·rə·bəl ′spās]
(mathematics)
A topological space which has a countable subset that is dense.
References in periodicals archive ?
Let ([OMEGA], [summation]) be a measurable space and Y be a separable metric space.
Y, where [OMEGA] is a complete measure space and Y is a complete separable metric space, is a measurable multivalued map, then [?
6 Any separable metric space admits an isometric embedding into Q.
2) X is a sequence-covering, compact-covering image of a separable metric space,
3) X is a compact-covering image of a separable metric space,
To make this question precise, we must consider the distal flows as points in a separable metric space.
Using the terminology of the previous section, this space is obtained by taking the free Banach space over a particular complete separable metric space known as the Urysohn space.
Related to characterizing a space X having a certain countable network P by an image of a separable metric space M under some covering-mapping f, many results have been obtained.
We asserted that if X is a connected separable metric space such that [[pi].
0]-space if and only if it is a compact-covering image of a separable metric space.
Gregoriades examines the equivalence classes under effective Borel isomorphism, between complete separable metric spaces that admit a recursive presentation, and show the existence of strictly increasing and strictly decreasing sequences as well as of infinite anti-chains under the natural notion of effective isomorphism reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.
Parthasarathy builds far in advance of the general theory of stochastic processes as the theory of probability measures in complete separable metric spaces.