2018
DOI: 10.1016/j.topol.2018.09.002
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Selective separability on spaces with an analytic topology

Abstract: We study two form of selective selective separability, SS and SS + , on countable spaces with an analytic topology. We show several Ramsey type properties which imply SS. For analytic spaces X, SS + is equivalent to have that the collection of dense sets is a G δ subset of 2 X , and also equivalent to the existence of a weak base which is an Fσ-subset of 2 X . We study several examples of analytic spaces.holds in general as shown by Barman-Dow [2]. However our proof is different. We analyze a space constructed… Show more

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Cited by 4 publications
(10 citation statements)
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“…Since each O n does not accumulate to x and x is a p − -point, there is E such that x ∈ E and E ∩ O n is finite for every n. Clearly E is a discrete subset of A. In summary, we have the following implications for countable regular spaces (see [6]).…”
Section: Preliminariesmentioning
confidence: 97%
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“…Since each O n does not accumulate to x and x is a p − -point, there is E such that x ∈ E and E ∩ O n is finite for every n. Clearly E is a discrete subset of A. In summary, we have the following implications for countable regular spaces (see [6]).…”
Section: Preliminariesmentioning
confidence: 97%
“…Let {A n : n ∈ N} be the sequence, given by Lemma 3.5, of pairwise disjoint finite subsets of X such that A := k∈E A k is dense in X. Since the topology of X is finer 6 than the topology of X(I), then A is dense in X(I). Let ϕ ∈ A ∪ {∅}.…”
Section: The Spaces X(i) and Y (I)mentioning
confidence: 99%
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“…Since we are mostly interested in definable ideals, we will work with analytic topologies, i.e., topologies τ on X such that τ is analytic as a subset of 2 X (see §4). The study of analytic topologies was initiated in [58] (see also [3,4,47,59,60,61,62]).…”
Section: Topological Representations By Nowhere Dense Setsmentioning
confidence: 99%
“…Since Q has a countable basis, then nwd(Q) is countably separated. On the other hand, nwd(CL(2 N )) is not weakly selective and therefore it is is not countably separated (see Example 3.9 in [3]). Thus a natural question is the following.…”
Section: Topological Representationmentioning
confidence: 99%