Abstract
This paper attempts to initiate the construction of a standardised basic theory of fuzzy topology. In general fuzziness is taken with respect to a complete lattice L satisfying the distributive law of finite meets over infinite joins, thus becoming a frame. When L is also continuous we define goodness in terms of the Scott topology following [Warner 1990], and insist on this as a minimal criterion in selecting standard fuzzy topological properties. For the closed unit interval, I, this reduces to Lowen’s goodness formulated in terms of lower semi-continuous functions [Lowen 1978].
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© 1993 Springer Science+Business Media Dordrecht
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Warner, M.W. (1993). Towards a Mathematical Theory of Fuzzy Topology. In: Lowen, R., Roubens, M. (eds) Fuzzy Logic. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2014-2_8
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DOI: https://doi.org/10.1007/978-94-011-2014-2_8
Publisher Name: Springer, Dordrecht
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