• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.263-286
• /
• 2016

We discuss relations between Galois coverings of compact Riemann surfaces and their Jacobi varieties. We prove a theorem of a kind of Galois correspondence for Abelian subvarieties of Jacobi varieties. We also prove a theorem on the sets of points in Jacobi varieties fixed by Galois group actions.

• Communications of the Korean Mathematical Society
• /
• v.17 no.2
• /
• pp.253-260
• /
• 2002

For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.657-663
• /
• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• Journal of the Chungcheong Mathematical Society
• /
• v.4 no.1
• /
• pp.75-84
• /
• 1991

In this paper, we introduce the concept of the fibrewise convergence space as a generalization of both the notion of fibrewise topology and that of convergence. Furthermore we observe the adjoint ness and Galois correspondence between the category of fibrewise topological spaces and the category of fibrewise convergence spaces. Finally we investigate the limit and colimit structures in these categories.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.2
• /
• pp.135-148
• /
• 2023

We prove that for any preordered intuitionistic fuzzy approximation space, an intuitionistic fuzzy topology can be created, and conversely, for any intuitionistic fuzzy topology, a reflexive intuitionistic fuzzy relation can be constructed. We also show that there is a relationship, called Galois correspondence, between the functors of these categories. Additionally, by applying certain limitations on the category of intuitionistic fuzzy topological spaces, we obtain an isomorphism between these categories.