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Hausdorff (quasi)topological MV-algebras
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In this paper, the relations between separation axioms and (quasi)topological MV-algebras are studied. It is proved that T0-spaces and (T1) Hausdorff spaces are equivalent in (quasi) topological MV-algebras. Also, some topologies on MV-algebras are generated by ideals, filters and prefilters. It is shown that the MV-algebras equipped with these topologies are (para)topological MV-algebras and (T0) normal spaces. In addition, some conditions are derived for locally compact Hausdorff MV-algebras to make them into normal paratopological MV-algebras. Finally, quotient MV-algebras are studied to get a Hausdorff topological quotient MV-algebra.
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Title: Hausdorff (quasi)topological MV-algebras
Description:
In this paper, the relations between separation axioms and (quasi)topological MV-algebras are studied.
It is proved that T0-spaces and (T1) Hausdorff spaces are equivalent in (quasi) topological MV-algebras.
Also, some topologies on MV-algebras are generated by ideals, filters and prefilters.
It is shown that the MV-algebras equipped with these topologies are (para)topological MV-algebras and (T0) normal spaces.
In addition, some conditions are derived for locally compact Hausdorff MV-algebras to make them into normal paratopological MV-algebras.
Finally, quotient MV-algebras are studied to get a Hausdorff topological quotient MV-algebra.
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