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**A note on weakly quasi continuous functions.**
*(English)*
Zbl 0863.54011

A function \(f:X\to Y\) is said to be weakly quasi continuous if for each \(x\in X\) each open set \(G\) containing \(x\) and each open set \(V\) containing \(f(x)\) there exists an open set \(U\) of \(X\) such that \(\emptyset\neq U\subset G\) and \(f(U)\subset \text{Cl}(G)\) [the reviewer and C. Stan, Stud. Cercet. Mat. 25, 41-43 (1973; Zbl 0255.54008)].

In this paper, the authors obtain some properties of weakly quasicontinuous functions and introduce the notion of weak* quasicontinuous functions.

From the “References” one can say that the authors do not know all the papers that have been published on these functions. So, many results are known and some are not correct. So: the “weakly semi-continuous functions” appear for the first time in [Gh. Costovici, Other elementary properties of the mappings of topological spaces, Bul. Inst. Politeh. Iaşi, Secţ. I 26(30), No. 3-4, 19-21 (1980)] as “semi weak continuous functions” and not in [S. P. Arya and M. P. Bhamini, Gaṇita 33, 124-134 (1982; Zbl 0586.54017)]. The “new type” of “weak quasicontinuous functions” appears for the first time in [A. Kar and P. Bhattacharyya, Weakly semi-continuous functions, J. Indian Acad. Math. 8, 83-93 (1986)] and is studied also in [A. Kar, Soochow J. Math. 15, 65-77 (1989; Zbl 0708.54006)].

On the proved properties, I specify that the results from Theorems 3.3 and 3.4 appear in [the reviewer and T. Noiri, Glas. Mat., III. Ser. 24(44), 391-399 (1989; Zbl 0707.54013)]. Theorem 3.15 is Theorem 4.12 from [Popa and Noiri, loc. cit.], Theorem 3.16 is a particular case of Theorem 4.8 from [Popa and Noiri, loc. cit.], Theorem 4.1 and Corollary 4.2 are particular cases of Theorem 4.1 from [Popa and Noiri, loc. cit.], Theorem 4.3 is Theorem 4.5 from [Popa and Noiri, loc. cit.], Corollary 4.4 is Corollary 4.11 from [Popa and Noiri, loc. cit.], Corollary 4.5 is a particular case of Theorem 4.6 from [Popa and Noiri, loc. cit.], Theorem 4.8 is a particular case of Theorem 4.1 of [Popa and Noiri, loc. cit.] and Theorem 6.6 is Theorem 3.4 from [Popa and Noiri, loc. cit.].

In this paper, the authors obtain some properties of weakly quasicontinuous functions and introduce the notion of weak* quasicontinuous functions.

From the “References” one can say that the authors do not know all the papers that have been published on these functions. So, many results are known and some are not correct. So: the “weakly semi-continuous functions” appear for the first time in [Gh. Costovici, Other elementary properties of the mappings of topological spaces, Bul. Inst. Politeh. Iaşi, Secţ. I 26(30), No. 3-4, 19-21 (1980)] as “semi weak continuous functions” and not in [S. P. Arya and M. P. Bhamini, Gaṇita 33, 124-134 (1982; Zbl 0586.54017)]. The “new type” of “weak quasicontinuous functions” appears for the first time in [A. Kar and P. Bhattacharyya, Weakly semi-continuous functions, J. Indian Acad. Math. 8, 83-93 (1986)] and is studied also in [A. Kar, Soochow J. Math. 15, 65-77 (1989; Zbl 0708.54006)].

On the proved properties, I specify that the results from Theorems 3.3 and 3.4 appear in [the reviewer and T. Noiri, Glas. Mat., III. Ser. 24(44), 391-399 (1989; Zbl 0707.54013)]. Theorem 3.15 is Theorem 4.12 from [Popa and Noiri, loc. cit.], Theorem 3.16 is a particular case of Theorem 4.8 from [Popa and Noiri, loc. cit.], Theorem 4.1 and Corollary 4.2 are particular cases of Theorem 4.1 from [Popa and Noiri, loc. cit.], Theorem 4.3 is Theorem 4.5 from [Popa and Noiri, loc. cit.], Corollary 4.4 is Corollary 4.11 from [Popa and Noiri, loc. cit.], Corollary 4.5 is a particular case of Theorem 4.6 from [Popa and Noiri, loc. cit.], Theorem 4.8 is a particular case of Theorem 4.1 of [Popa and Noiri, loc. cit.] and Theorem 6.6 is Theorem 3.4 from [Popa and Noiri, loc. cit.].

Reviewer: V.Popa (Bacau)

### MSC:

54C08 | Weak and generalized continuity |