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Conjunctivity in quantales

Quantales can be viewed as a framework for noncommutative topology. The notion of a w-quantale is defined. Conjunctivity in quantales is developed. Weakly dually atomic w-quantales are characterized. Normal quantales are considered. Any normal quantale is a preliminary w-quan­ tale. Any dually atomic normal quantale is a frame. An explicit description of the regular coreflection of a certain class of normal quantales is given.