Year 2019, Volume 48 , Issue 6, Pages 1761 - 1766 2019-12-08

On selective sequential separability of function spaces with the compact-open topology

Alexander V. OSİPOV [1]


For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on $X$ with the compact-open topology. A subset $A\subset X$ is said to be sequentially dense in $X$ if every point of $X$ is the limit of a convergent sequence in $A$. A space $C_k(X)$ is selectively sequentially separable (in Scheepers' terminology: $C_k(X)$ satisfies $S_{fin}(\mathcal{S},\mathcal{S})$) if whenever $(S_n : n\in \mathbb{N})$ is a sequence of sequentially dense subsets of $C_k(X)$, one can pick finite $F_n\subset S_n$ ($n\in \mathbb{N}$) such that $\bigcup \{F_n: n\in \mathbb{N}\}$ is sequentially dense in $C_k(X)$. In this paper, we give a characterization for $C_k(X)$ to satisfy $S_{fin}(\mathcal{S},\mathcal{S})$.
compact-open topology, function space, selectively sequentially separable, S1(S, S), sequentially dense set, property 2, property 4
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-6460-1943
Author: Alexander V. OSİPOV (Primary Author)
Institution: Ural State University of Economics
Country: Russian Federation


Dates

Publication Date : December 8, 2019

Bibtex @research article { hujms479607, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1761 - 1766}, doi = {10.15672/HJMS.2018.635}, title = {On selective sequential separability of function spaces with the compact-open topology}, key = {cite}, author = {V. OSİPOV, Alexander} }
APA V. OSİPOV, A . (2019). On selective sequential separability of function spaces with the compact-open topology. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1761-1766 . DOI: 10.15672/HJMS.2018.635
MLA V. OSİPOV, A . "On selective sequential separability of function spaces with the compact-open topology". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1761-1766 <https://dergipark.org.tr/en/pub/hujms/issue/50516/479607>
Chicago V. OSİPOV, A . "On selective sequential separability of function spaces with the compact-open topology". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1761-1766
RIS TY - JOUR T1 - On selective sequential separability of function spaces with the compact-open topology AU - Alexander V. OSİPOV Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2018.635 DO - 10.15672/HJMS.2018.635 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1761 EP - 1766 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.635 UR - https://doi.org/10.15672/HJMS.2018.635 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On selective sequential separability of function spaces with the compact-open topology %A Alexander V. OSİPOV %T On selective sequential separability of function spaces with the compact-open topology %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2018.635 %U 10.15672/HJMS.2018.635
ISNAD V. OSİPOV, Alexander . "On selective sequential separability of function spaces with the compact-open topology". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1761-1766 . https://doi.org/10.15672/HJMS.2018.635
AMA V. OSİPOV A . On selective sequential separability of function spaces with the compact-open topology. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1761-1766.
Vancouver V. OSİPOV A . On selective sequential separability of function spaces with the compact-open topology. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1766-1761.