Notes on Strongly Semi-Closed Graph

Authors: Alkhazragy A., Al-Hachami A.K.H., Mayah F. Published: 23.06.2022
Published in issue: #3(102)/2022  
DOI: 10.18698/1812-3368-2022-3-17-27

Category: Mathematics and Mechanics | Chapter: Substantial Analysis, Complex and Functional Analysis  
Keywords: closed graph, semi-closed graph, strongly semi-closed graph


In these papers, we study on mapping with strongly semi-closed graph. We first introduce the notion "strongly semi-closed graph" in analogue to the closed graph. Also, we study some of their basic properties. This study proved that: If Y is extremally s-disconnected semi-T2-space and f : X → Y is a set-s-connected surjection, then G(f) is semi-closed. If Y is Hausdorff space and f is almost semi continuous, then G(f) is strongly semi-closed. If Y is semi-T2-space and f is irresolute, then G(f) is strongly semi-closed. Semi-closed mapping and semi-closed graph are two separate concepts. If G(f) is a semi-closed and f is surjection(onto), then Y is semi-T1-space. If the injective S**-open map X is semi**-connected and G(f) is semi-closed then X is semi-T2-space provided it is T1-space and locally semi-connected. S**-closed mapping and semi-closed graph are two separate concepts. If Y is semi-regular space, then the following are equivalent G(f) is semi-closed and G(f) is strongly semi-closed

Please cite this article as:
Alkhazragy A., Al-Hachami A.K.H., Mayah F. Notes on strongly semi-closed graph. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2022, no. 3 (102), pp. 17--27. DOI: https://doi.org/10.18698/1812-3368-2022-3-17-27


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