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On Extensions of Continuous Functions
Yoon, Sam-Youl,Park, Sang-Ho 慶尙大學校 기초과학연구소 1991 基礎科學硏究所報 Vol.7 No.-
본 논문에서 위상공간 X와 환 C(S)=[f|f:X→R은 연속함수}사이의 관계를 연구하고, 이를 바탕으로 이미 잘 알려진 정규공간에서 Tietze의 확장 정리를 증명하여 보았다. 그리고, 일반적인 위상공간 X의 부분공간 S가 C-embedded이기 위한 조건을 연구하여, 다음과 같은 결과를 얻었다. 1. 완전정칙공간 X에서의 모든 compact 집합 S는 C-embedded이다. 2. X와 Y가 위상공간이고 S⊂X라고 하자. h|s가 open injection인 함수 h∈C(X,Y)가 존재할 때 h(S)가 h(X)에서 C-embedded일 필요충분조건은 h(S)가 h(X)에서 C-embedded이면 S는 X에서 C-embedded이다. 3. X와 Y가 위상공간이고 S⊂X라고 하자. open injection인 함수 h∈C(X,Y)가 존재할 때 S가 X에서 C-embedded일 필요충분조건은 h(S)가 h(X)에서 C-embedded이다. 4. X가 위상공간이고 Y는 정규공간이고, S⊂X라고 하자. S가 Y의 폐집합 H와 위상동형이 되게 하는 h∈C(X,Y)가 존재하면 S는 X에서 C-embedded이다. 단, 여기서 C(X,Y)={h|h : X-→는 연속함수}이고 h|S는 h의 S에서 제한 사상이다. In this paper, we study relations between a topological space X and the ring C(X) of all real valued continuous functions on X, in particular, C-embedding, C-embedding and Tietze's extension theorem. Also, we obtain some sufficient conditions for a subset to be C-embedded.
Sam-Youl Yoon,Chung Yun Kim,Hyung Joon Han,Kun Ok Lee,Tae-Jin Song 대한외과학회 2015 Annals of Surgical Treatment and Research(ASRT) Vol.88 No.5
Purpose: The efficiency of ischemic postconditioning (IPC) was evaluated in a rat model of ischemic liver. Concentration of survivin of liver tissue correlated with the degree of antiapoptosis, so survivin was estimated to evaluate the efficiency of IPC on ischemic reperfusion (IR) injury. Methods: Twenty-four healthy rats were divided to three groups (SHAM, IR, and IPC). Rats in the SHAM group displayed no change during 3 hours. Rats in the IR group were ischemic within 1 hour of clamping the left hepatic artery and left portal vein. Reperfusion for 2 hours was then done. IPC group, intermittent 2, 3, 5, and 7 minutes of reperfusion followed by 1 hour of warm ischemia. Two-minute reocclusion was done after each reperfusion. Rat sera were analyzed for AST and ALT, and Western blot analysis of rat liver tissue of rats evaluated malondialdehyde (MDA) and survivin. Results: MDA in the liver tissue of rats in the IR and IPC group were significantly high than in the liver tissue of the SHAM group (P = 0.003 and P = 0.008, respectively). Survivin was higher in the IPC group than in the SHAM and IR groups (P = 0.021 and P = 0.024, respectively). Conclusion: IPC could not prevent lipid oxidation in liver cell mitochondria, but did aid in the regeneration of ischemic injured liver cells. The results indicate that IPC can suppress the apoptosis of liver cells and reduce reperfusion injury of liver tissue.