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Fixed points with respect to the L-slice homomorphism $σ_{a}$

K.S. Sabna; N.R. Mangalambal — 2019

Archivum Mathematicum

Given a locale $L$ and a join semilattice $J$ with bottom element $0_{J}$ , a new concept $(σ, J)$ called $L$ -slice is defined,where $σ$ is as an action of the locale $L$ on the join semilattice $J$ . The $L$ -slice $(σ, J)$ adopts topological properties of the locale $L$ through the action $σ$ . It is shown that for each $a \in L$ , $σ_{a}$ is an interior operator on $(σ, J)$ .The collection $M = {σ_{a}; a \in L}$ is a Priestly space and a subslice of $L$ - $Hom (J, J)$ . If the locale $L$ is spatial we establish an isomorphism between the $L$ -slices $(σ, L)$ and $(δ, M)$ . We have shown that the fixed set of $σ_{a}$ ,...

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