Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903951 | Topology and its Applications | 2018 | 16 Pages |
Abstract
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 λX which is weakly Lindelöf containing X as a dense subspace on which every fâC(X) with Lindelöf cozero-set can be extended (when this is the case, we say that X is CL-embedded). Next, using this space, we present the largest Lindelöf subspace ÎX of βX in which X is CL-embedded. If X is locally Lindelöf, λX coincides with ÎX and it turns out in this case that ÎX(=λX) is the smallest Lindelöf subspace of βX with compact remainder. Using the structure of ÎX, we also give the smallest realcompact subspace ÏX of βX with compact remainder. Finally the relations between the spaces Ï
X, λX, ÏX, ÎX and βX are investigated and we apply the structures of these spaces to characterize some intersections of free maximal ideals of C(X).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
F. Azarpanah, A.A. Hesari, A.R. Salehi, A. Taherifar,