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A note on mappings of extremally disconnected spaces. (English) Zbl 0597.54037

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 T. Noiri [Czech. Math. J. 31(106), 314-321 (1981; Zbl 0483.54006)].
Reviewer: A.Blaszczyk

MSC:

54G05 Extremally disconnected spaces, \(F\)-spaces, etc.
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54A05 Topological spaces and generalizations (closure spaces, etc.)

Citations:

Zbl 0483.54006
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Full Text: DOI

References:

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