Abstract
In chapter 3, filters of lattice implication algebras have been studied from algebraic viewpoint. In this chapter, a topological space based on filters of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed. In the sequel, the product topology and quotient topology for filter spaces are studied. Finally, the prime spaces for lattice implication algebras and topological lattices generated by filters are presented.
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© 2003 Springer-Verlag Berlin Heidelberg
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Xu, Y., Qin, K., Ruan, D., Liu, J. (2003). Topological Structure of Filter Spaces. In: Lattice-Valued Logic. Studies in Fuzziness and Soft Computing, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44847-1_6
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DOI: https://doi.org/10.1007/978-3-540-44847-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07279-6
Online ISBN: 978-3-540-44847-1
eBook Packages: Springer Book Archive