Popa, Valeriu; Noiri, Takashi On \(m\)-continuous multifunctions. (English) Zbl 1049.54507 Bul. Științ. Univ. Politeh. Timiș., Ser. Mat.-Fiz. 46(60), No. 2, 1-12 (2001). Summary: The authors define a multifunction \(F\colon X\to Y\) to be \(m\)-continuous if for each point \(x\in \) and any open subsets \(G_1,G_2\) of \(Y\) such that \(F(x)\subset G_1\) and \(F(x)\cap G_2\neq\emptyset\) there exists an \(m\)-open subset \(U\) of \(X\) containing \(x\) such that \(F(U)\subset\text{Cl}\,(G_1)\) and \(F(u)\cap\text{Cl}\,(G_2)\neq\emptyset\) for every \(u\in U\). The functions enable us to unify continuity, \(\alpha\)-continuity, quasi-continuity, precontinuity, and \(\beta\)-continuity for multifunctions. Some characterizations and several properties concerning \(m\)-continuous multifunctions are obtained. Cited in 1 Review MSC: 54C60 Set-valued maps in general topology 54C08 Weak and generalized continuity Keywords:minimal structure; \(m\)-open; \(m\)-continuous; multifunction PDFBibTeX XMLCite \textit{V. Popa} and \textit{T. Noiri}, Bul. Științ. Univ. Politeh. Timiș., Ser. Mat.-Fiz. 46(60), No. 2, 1--12 (2001; Zbl 1049.54507)