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Continuity of Function Spaces from Pointwise Directed Families of Characteristic Functions

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Abstract

In earlier work the second author introduced the tool of pointwise directed families of characteristic functions to establish that certain continuous function spaces [X → Q] were continuous domains. In this paper we extend those earlier results, while significantly simplifying and refining the machinery involved. Our main result asserts that the function space [X → Q] is a continuous dcpo if X is locally compact and coherent and Q is a retract of a bifinite domain (RB-domain) with ⊥.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Jimmie Lawson

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Xiaoyong Xi

Authors
  1. Jimmie Lawson
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  2. Xiaoyong Xi
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Corresponding author

Correspondence to Jimmie Lawson.

Additional information

The work of the second author was supported by NSFC (No. 11361028; 61300153).

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Lawson, J., Xi, X. Continuity of Function Spaces from Pointwise Directed Families of Characteristic Functions. Order 32, 409–418 (2015). https://doi.org/10.1007/s11083-014-9341-9

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  • DOI: https://doi.org/10.1007/s11083-014-9341-9

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