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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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