Construction of a Subspace of the Spectrum of L From the L-Slice for a Locale L - Sabna, Kochanamkulangara Sulaiman; Mangalambal, Natuvil Madhom Rama Iyer (Sarajevo Journal of Mathematics, 2024)
The notion of compactness in the L-slice (σ,J) of a locale L is introduced and we show that L-slice compactness is stronger than topological compactness and localic compactness. A subspace Y , of the spectrum Sp(L) of the locale L , is constructed using filters F_x={a L: σ(a,x)=x} for compact elements x (σ,J) and the compactness of the subspace Y is characterised using the existence of a maximal compact element in the L-slice (σ,J) .