A note on mappings of extremally disconnected spaces
type: Item
instance of: scholarly article
title: A note on mappings of extremally disconnected spaces
zbMATH Open document ID: 0597.54037
DOI: 10.1007/BF01961010
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 54G05
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54A05
zbMATH DE Number: 3962736
zbMATH Keywords: semi-open sets
zbMATH Keywords: pre-open sets
zbMATH Keywords: \(\alpha \) -sets
zbMATH Keywords: \(\alpha \) -topologies
zbMATH Keywords: semi-continuous mappings
zbMATH Keywords: pre-open mappings
zbMATH Keywords: images of extremally disconnected spaces
author: Dragan Janković
reviewed by: Aleksander Błaszczyk
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01961010
OpenAlex ID: W2140209629
description: scientific article; zbMATH DE number 3962736