A new approach to nearly paracompact spaces

  • A. Mukharjee Department of Mathematics, Bankura University, Bankura, W. Bengal- 722 155

Анотація

The pre-open sets are a generalization of open sets of topological spaces. In this paper, we introduce and study a notion of po-paracompact spaces via pre-open sets on topological spaces. We see that po-paracompact spaces are equivalent to nearly paracompact spaces. However, we find new characterizations to nearly paracompact spaces when we study it in the sense of poparacompact spaces. We see that a topological space is nearly paracompact if and only if each regularly open cover of the topological space has a locally finite pre-open refinement. We also show that four statements involving pre-open sets on an almost regular topological space are equivalent. A result on a subspace of a topological space is also obtained in term of pre-open sets.

Біографія автора

A. Mukharjee, Department of Mathematics, Bankura University, Bankura, W. Bengal- 722 155

Department of Mathematics, Bankura University, Bankura, W. Bengal- 722 155

Посилання

K. Al-Zoubi, S. Al-Ghour, On P3-paracompact spaces, Int. J. Math. Math. Sci., (2007), Article ID 80697, 12 p., doi: 10.1155/2007/80697.

H.H. Corson, E. Michael, Metrizability of certain countable unions, Illinois J. Math., 8 (1964), 351–360.

A.S. Mashhour, M.E. Abd El-Monsef, S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53 (1982), 47–53.

A.S. Mashhour, M.E. Abd El-Monsef, I.A. Hasanein, On pretopological spaces, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 28(76) (1984), 39–45.

A.S. Mashhour, I.A. Hasanein, S.N. El-Deeb, A note on semicontinuity and precontinuity, Indian J. Pure Appl. Math., 13 (1982), №10, 1119–1123.

K.B. Bagchi, A. Mukharjee, M. Paul, A new approach to nearly compact spaces, Acta Comment. Univ. Tartu. Math., 22 (2018), №1, 137–147, doi: 10.12697/ACUTM.2018.22.12.

M.K. Singal, S.P. Arya, On nearly paracompact spaces, Mat. Vesnik, 6 (1969), 3–16.

M.K. Singal, S.P. Arya, On almost-regular spaces, Glas. Mat. Ser. III, 4 (1969), №24, 89–99.

S. Willard, General topology, Dover Publications, Inc., New York, 2004.

Опубліковано
2023-12-18
Як цитувати
Mukharjee, A. (2023). A new approach to nearly paracompact spaces. Математичні студії, 60(2), 201-207. https://doi.org/10.30970/ms.60.2.201-207
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