TY - JOUR
ID - 242304
TI - Some Properties of Complete Boolean Algebras
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Molkhasi, Ali
AD - Department of Mathematics, Faculty of Science, University of Farhangian , Tabriz, Iran.
Y1 - 2021
PY - 2021
VL - 18
IS - 2
SP - 63
EP - 71
KW - $q^prime$-compactness
KW - Strongly algebraically closed algebras
KW - Complete Boolean algebras
DO - 10.22130/scma.2020.127693.802
N2 - The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all real-valued continuous functions and the equivalence classes of $lambda$-measurable. We shall provide conditions which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice and $(B,, sigma)$ is a Hausdorff space and $B$ satisfies the $G_sigma$ property, then $B$ carries a strictly positive Maharam submeasure.
UR - https://scma.maragheh.ac.ir/article_242304.html
L1 - https://scma.maragheh.ac.ir/article_242304_dd36edfbe215f4011e11996eac789ce2.pdf
ER -