A Note on Semi-Closed Graph

Abstract

이 논문에서 사상이 반폐그래프를 갖기 위한 여러가지 조건들을 알아본다. 사상이 폐그래프를 가지?? 그 그래프는 반폐 그래프이나, 그 역은 성립하지 않음을 보인다. 또 이미 알려진 몇 개의 사상들이 반폐 그래프를 갖지 못하는 것을 보이고, 반면, 반폐 그래프를 가져도 항상 좋은 형의 사상이 되지 않음을 보였다.

In this note, various conditions are discussed under which a mapping has a semi-closed graph. If a mapping has a closed graph, then, clearly, its graph is semi0closed but not conversely (Exmaple 1). It is shown that, on one hand, various types of some known mappings may fail to have semi-closed graphs and, on the other hand, a mapping having semi-closed graph may fail to be some 'nice' types of mappings.

In this note, various conditions are discussed under which a mapping has a semi-closed graph. If a mapping has a closed graph, then, clearly, its graph is semi0closed but not conversely (Exmaple 1). It is shown that, on one hand, various types of some known mappings may fail to have semi-closed graphs and, on the other hand, a mapping having semi-closed graph may fail to be some 'nice' types of mappings.