A Lindelofication

作者：Azarpanah F; Hesari A A; Salehi A R^*; Taherifar A

来源：Topology and Its Applications, 2018, 245: 46-61.

DOI：10.1016/j.topol.2018.06.009

• Lindelofication
• Locally Lindelof
• Almost real maximal ideal
• Realcompactification
• Weakly Lindelof
• C-L-embedded
• I-pseudocompact

An almost real maximal ideal M of C(X) is a maximal ideal that is either fixed or Z[M] contains a free z-filter which is closed under countable intersection. Using these maximal ideals, we first construct a space lambda X which is weakly Lindelof containing X as a dense subspace on which every f is an element of C(X) with Lindelof cozeroset can be extended (when this is the case, we say that X is C-L-embedded). Next, using this space, we present the largest Lindelof subspace Lambda X of beta X in which X is C-L-embedded. If X is locally Lindelof, lambda X coincides with Lambda X and it turns out in this case that Lambda X(= lambda X) is the smallest Lindelof subspace of beta X with compact remainder. Using the structure of lambda X, we also give the smallest realcompact subspace Upsilon X of beta X with compact remainder. Finally the relations between the spaces upsilon X, lambda X, Upsilon X, lambda X and beta X are investigated and we apply the structures of these spaces to characterize some intersections of free maximal ideals of C(X).

• 出版日期2018-8-15
• 单位中国石油大学（北京）