Completely prime L-filters,irreducible L-filters and sobriety |
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Authors: | Gunther Jäger Wei Yao |
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Affiliation: | 1. Department of Mechanical Engineering, University of Applied Sciences Stralsund, 18435 Stralsund, Germany;2. Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China |
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Abstract: | In this paper, for a frame L, we characterize modified sobriety in stratified L-topological spaces and strong L-topological spaces internally using certain classes of stratified L-filters. While the first characterization using completely prime L-filters is trivial and applies to all stratified L-topological spaces, the other one using irreducible L-filters generalizes an approach of R.E. Ho?mann to the lattice-valued case but is restricted to either the case that the lattice is a complete Boolean algebra or to the case of completely distributive lattices and strong L-topological spaces. |
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Keywords: | 54E70 54A20 |
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