Insertion and extension theorems for lattice-valued functions on preordered topological spaces |
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Authors: | J Gutiérrez García I Mardones-Pérez MA de Prada Vicente |
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Institution: | Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain |
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Abstract: | In this paper, the possibility of inserting an increasing continuous lattice-valued function between two comparable semicontinuous functions is studied. First, we obtain a sufficient condition for such insertion, then we get new characterizations of several classes of preordered topological spaces, among them normally preordered and extremally preorder-disconnected spaces. Conditions for the continuous and increasing extension of lattice-valued maps of the same type defined on closed (resp. open) sets are also investigated. |
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Keywords: | Insertion Extension Completely distributive lattice Semicontinuous function Preordered topological space |
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