TY - JOUR
AU1 - Farley, J. D.
AB -  Let X be a poset and Y an ordered space; X

Y



$(X^Y_\Sigma, X^Y_\Lambda)$
 denotes the poset of continuous order-preserving maps from Y to X with the discrete (respectively, Scott, Lawson) topology. If S is a 

$\lor$
-semilattice, 

$S^\sigma$
 its ideal semilattice, and T a bounded distributive lattice with Priestley dual space P(T), it is shown that the following isomorphisms hold: 

$(S^{P(T)})^\sigma \cong (S^\sigma) ^{P(T^\sigma)}_\Lambda.$
 Moreover, 

$$(S^\sigma)^{P(T^\sigma)}_\Lambda \cong (S^\sigma) ^{P(T^\sigma)}$ if and only if $(S^\sigma)^{P(T^\sigma)}_\Lambda = (S^\sigma)^{P(T^\sigma)},$
 and sufficient conditions and necessary conditions for the isomorphism to hold are obtained (both necessary and sufficient if S is a distributive 

$\lor$
-semilattice).

TI - Ideals of Priestley powers of semilattices
JF - algebra universalis
DO - 10.1007/s000120050114
DA - 1999-09-01
UR - https://www.deepdyve.com/lp/springer-journals/ideals-of-priestley-powers-of-semilattices-nAF4wcNyhg
SP - 239
EP - 254
VL - 41
IS - 4
DP - DeepDyve
ER -