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The attainable spaces and its analogues (in Ukrainian) |
| Author |
O. V. Maslyuchenko
ovmasl@gmail.com
×åðí³âåöüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ Þ. Ôåäüêîâè÷à
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| 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 quasi-continuous 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 set-theoretic 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)
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| Pages |
98-105 |
| Volume |
37 |
| Issue |
1 |
| Year |
2012 |
Journal |
Matematychni Studii |
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