An extension of Pontryagin duality

B. J. Day*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Let V denote the symmetric monoidal closed category of limit-space abelian groups and let L denote the full subcategory of locally compact Hausdorff abelian groups. Results of Samuel Kaplan on extension of characters to products of L–groups are used to show that each closed subgroup of a product of L-groups is a limit of L–groups. From this we deduce that the limit closure of L in V is reflective in V and has every group Pontryagin reflexive with respect to the structure of continuous convergence on the character groups. The basic duality L ≃ Lop is then extended.

    Original languageEnglish
    Pages (from-to)445-456
    Number of pages12
    JournalBulletin of the Australian Mathematical Society
    Volume19
    Issue number3
    DOIs
    Publication statusPublished - 1978

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