Properties of quasi-precontinuous functions
type: Item
instance of: scholarly article
title: Properties of quasi-precontinuous functions
zbMATH Open document ID: 0871.54017
author: Yanyan Li
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1997-10-05T00:00:00Z
review text: A subset \(A\) of a topological space \(X\) is called preopen if \(A\subset \text{Int(Cl} (A))\). A function \(f:X\to Y\) is called quasi-precontinuous [the authors, Quasi-pre-continuous functions, J. Indian Acad. Math. 14, No. 2, 115-126 (1992)] if for each \(x\in X\) and each open set \(V\) containing \(f(x)\) there exists a preopen set \(U\) containing \(x\) such that \(f(U) \subset \text{Cl} (V)\). Recently, the reviewer and \textit{T. Noiri} [Demonstr. Math. 25, No. 1/2, 241-251 (1992; Zbl 0789.54014), Theorem 3.1] showed that quasi-precontinuity is equivalent to almost weak continuity due to \textit{D. S. Janković} [Int. J. Math. Math. Sci. 8, 615-619 (1985; Zbl 0577.54012)]. The authors study some properties of quasi precontinuous functions and the reviewer emphasizes that they are also properties of weakly almost continuous functions. But almost all of them are already known, as they appeared either in the above mentioned paper of Popa and Noiri or in [\textit{T. Noiri}, Int. J. Math. Math. Sci. 10, 97-111 (1987; Zbl 0617.54008)] or in [\textit{T. Noiri} and \textit{V. Popa}, Demonstr. Math. 26, No. 2, 363-380 (1993; Zbl 0859.54007)]. So Theorem 3.1 is a mixture of some sentences from Theorem 3.1 of [Noiri, loc. cit.] and Theorem 3.1 of [Popa and Noiri, [loc. cit.]. Theorem 4.1 is Theorem 3.7 from [Popa and Noiri, loc. cit.]. Theorem 4.2 is Theorem 6.3.5 from [Noiri, loc. cit.]. Theorem 4.7 is a particular case of Theorem 7.2 from [Noiri and Popa, loc. cit.]. Theorem 4.8 is a particular case of Theorem 7.1 from [Noiri and Popa, loc. cit.]. Theorem 5.5 is Theorem 5.6 from [Popa and Noiri, [loc. cit.]. Corollary 5.7 is Theorem 5.1 from [Popa and Noiri, loc. cit.]. Theorem 6.1 is a consequence of Theorem 6.1 from [Noiri and Popa, loc. cit.]. Theorem 6.2 is a particular case of Corollary 5.3 from [Noiri and Popa, loc. cit.]. Theorem 6.3 is a particular case of Theorems 4.6 and 4.8 from [Noiri and Popa, loc. cit.]. From the ``References'' results that the authors…
reviewed by: Valeriu Popa
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 903327
MaRDI profile type: Publication
Recommended article: ALMOST WEAKLY CONTINUOUS FUNCTIONS
Recommended article: ON ALMOST WEAKLY CONTINUOUS FUNCTIONS
Recommended article: Q3357073
Recommended article: On a weak form of almost weakly continuous functions
Recommended article: On almost precontinuous functions
Recommended article: A note on weakly quasi continuous functions
Recommended article: Properties of prealmost \(\alpha\)-continuous and presemi-weakly continuous functions
Recommended article: On \(\theta\)-precontinuous functions
Recommended article: Q4359779
Recommended article: Q3646756
description: scientific article; zbMATH DE number 903327