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Weakly algebraic ideal topology of effect algebras. (English) Zbl 1354.06003

Summary: In this paper, we show that every weakly algebraic ideal of an effect algebra \(E\) induces a uniform topology (weakly algebraic ideal topology, for short) with which \(E\) is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation \(\oplus\) of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation \(\ominus\) of effect algebras and the operations \(\wedge\) and \(\vee\) of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.

MSC:

06B10 Lattice ideals, congruence relations
03G12 Quantum logic
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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