
The attainable spaces and its analogues (in Ukrainian) 
Author 
O. V. Maslyuchenko
ovmasl@gmail.com
×åðí³âåöüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ Þ. Ôåäüêîâè÷à

Abstract 
In this paper we investigate interplays between several type of the attainable spaces. We
introduce the class of discreetly saturated spaces which contains all metrizable spaces and
all hereditarily separable perfectly normal spaces and check that a first countable discreetly
saturated space has all type of attainability. We also obtain that weakly discreetly attainable
spaces are countably resolvable. 
Keywords 
attainable space; pairwise attainable space; discreetly attainable space; pairwise discreetly attainable
space; weakly attainable space; weakly pairwise attainable space; weakly discretely attainable space;
weakly/ pairwise discreetly attainable space 
Reference 
1. Maslyuchenko O.V. The oscillation of separately continuous functions and topological games: Dis. ...
kand. fiz.mat. nauk: 01.01.01. – Chernivtsi, 2002. – 149 p. (in Ukrainian)
2. Maslyuchenko O.V. Construction of $\omega$primitives: strongly attainable spaces// Matematychnyj visnyk
NTSh. – 2009. – V.6. – P. 155–178. (in Ukrainian)
3. Maslyuchenko O.V. The oscillation of quasicontinuous functions on pairwise attainable spaces// Houston
Journal of Mathematics – 2009. – V.35, ¹1. – P. 113–130.
4. Engelking R. General topology. – Warszawa: PWN, 1977. – 626 p.
5. Hewitt E. A problem of settheoretic topology// Duke Math. J. – 1943. – V.10, ¹2. – P. 309–333.
6. Protasov I.V. Resovability of groops// Mat. Stud. – 1998. – V.9, ¹2. – P. 130–148. (in Russian)

Pages 
98105 
Volume 
37 
Issue 
1 
Year 
2012 
Journal 
Matematychni Studii 
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