A note on mappings of extremally disconnected spaces
The author studies relationships between various generalizations of continuous mappings and open mappings. In particular semi-continuous and pre-open mappings are studied. A mapping f:X\(\to Y\) is called semi- continuous if \(f^{-1}(U)\subset cl Int f^{-1}(U)\) for every open set \(U\subset Y\) whereas it is pre-open if f(V)\(\subset Int cl f(V)\) for every open set \(V\subset X\). One of the main theorems of this paper says that images of extremally disconnected spaces under semi-continuous pre- open mappings remain extremally disconnected. This improves a result of \textit{T. Noiri} [Czech. Math. J. 31(106), 314-321 (1981; Zbl 0483.54006)].
images of extremally disconnected spaces
scientific article; zbMATH DE number 3962736
scientific article