• 충청수학회지
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• 제22권4호
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• pp.689-697
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• 2009

We study the existence of surjective morphisms between Fano manifolds of Picard number 1, when the source is given by the intersection of a cubic hypersurface and either a quadric or another cubic hypersurface in a projective space.

• 대한수학회논문집
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• 제33권2호
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• pp.561-569
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• 2018

In this paper, we introduce some notions of orthogonality in the setting of Finsler $C^*$-modules and investigate their relations with the Birkhoff-James orthogonality. Suppose that ($E,{\rho}$) and ($F,{\rho}^{\prime}$) are Finsler modules over $C^*$-algebras $\mathcal{A}$ and $\mathcal{B}$, respectively, and ${\varphi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a *-homomorphism. A map ${\Psi}:E{\rightarrow}F$ is said to be a ${\varphi}$-morphism of Finsler modules if ${\rho}^{\prime}({\Psi}(x))={\varphi}({\rho}(x))$ and ${\Psi}(ax)={\varphi}(a){\Psi}(x)$ for all $a{\in}{\mathcal{A}}$ and all $x{\in}E$. We show that each ${\varphi}$-morphism of Finsler $C^*$-modules preserves the Birkhoff-James orthogonality and conversely, each surjective linear map between Finsler $C^*$-modules preserving the Birkhoff-James orthogonality is a ${\varphi}$-morphism under certain conditions. In fact, we state a version of Wigner's theorem in the framework of Finsler $C^*$-modules.

• 대한수학회보
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• 제55권4호
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• pp.1023-1035
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• 2018

We strengthen a result of Michiel Kosters by proving the following theorems: (*) Let ${\phi}:W{\rightarrow}V$ be a finite surjective morphism of algebraic varieties over an ample field K. Suppose V has a simple K-rational point a such that $a{\not\in}{\phi}(W(K_{ins}))$. Then, card($V(K){\backslash}{\phi}(W(K))$ = card(K). (**) Let K be an infinite field of positive characteristic and let $f{\in}K[X]$ be a non-constant monic polynomial. Suppose all zeros of f in $\tilde{K}$ belong to $K_{ins}{\backslash}K$. Then, card(K \ f(K)) = card(K).

• 한국수학교육학회지시리즈A:수학교육
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• 제16권2호
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• pp.22-26
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• 1978

($\alpha$$_{x}$, $\alpha$X)와 ($\alpha$$_{Y}$ , $\alpha$Y)를 T$_2$ 공간 X와 Y의 Alexandroff base Compactification이라 할 때 $\alpha$fㆍ$\alpha$$_{x}$=$\alpha$$_{Y}$ f를 만족하는 open이고 연속인 함수 $\alpha$f:$\alpha$X$\longrightarrow$$\alpha$Y가 존재하는 연속함수 f:X$\longrightarrow$Y는 유일한 $\alpha$-extension $\alpha$f를 가지며 Category ABC를 T$_2$ 공간과 위와 같은 연속함수 f들의 Category라고 할 때 open이고 연속인 함수와 Compact space들의 Category는 Category ABC의 epireflective subcategory임을 밝혔다.