Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.springerlink.com/content/231n27j3p4108k86/ |
| Field | General mathematics |
| Keywords | ompact element; Compactly generated; de Morgan lattice; Basic algebra; Lattice effect algebra |
| Description | We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L Moreover, if L is complete then L is (o)-topological Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated. |
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