TY - JOUR
T1 - Strongly sequentially separable function spaces, via selection principles
AU - Osipov, Alexander V.
AU - Szewczak, Piotr
AU - Tsaban, Boaz
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continuous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.
AB - A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continuous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.
KW - (ΩΓ)
KW - (ΩΓ)
KW - Borel function
KW - C-Space
KW - Function spaces
KW - Gerlits–Nagy
KW - Selection principles
KW - Strong sequential separability
KW - γ-Property
KW - γ-Set
UR - http://www.scopus.com/inward/record.url?scp=85074982012&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2019.106942
DO - 10.1016/j.topol.2019.106942
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AN - SCOPUS:85074982012
SN - 0166-8641
VL - 270
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 106942
ER -