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Rigid extensions of ℓ-groups of continuous functions

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Abstract

Let C(X, ℤ), C(X, ℂ) and C(X) denote the ℓ-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for the extensions C(X, ℤ) ⩽ C(X, ℚ) ⩽ C(X) to be rigid, major, and dense.

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Authors and Affiliations

  1. Department of Mathematics, Midwestern State University, 3410 Taft Blvd., Wichita Falls, TX, 76308, USA

    Michelle L. Knox

  2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Warren Wm. McGovern

Authors
  1. Michelle L. Knox
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  2. Warren Wm. McGovern
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Correspondence to Michelle L. Knox.

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Knox, M.L., McGovern, W.W. Rigid extensions of ℓ-groups of continuous functions. Czech Math J 58, 993–1014 (2008). https://doi.org/10.1007/s10587-008-0064-1

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  • DOI: https://doi.org/10.1007/s10587-008-0064-1

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