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Products of protopological groups

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  • Julie C. Jones

Abstract

Montgomery and Zippin saied that a group is approximated by Lie groups if every neighborhood of the identity contains an invariant subgroup H such that G / H is topologically isomorphic to a Lie group. Bagley, Wu, and Yang gave a similar definition, which they called a pro-Lie group. Covington extended this concept to a protopological group. Covington showed that protopological groups possess many of the characteristics of topological groups. In particular, Covington showed that in a special case, the product of protopological groups is a protopological group. In this note, we give a characterization theorem for protopological groups and use it to generalize her result about products to the category of all protopological groups.

Suggested Citation

  • Julie C. Jones, 2001. "Products of protopological groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 28, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:375230
    DOI: 10.1155/S016117120100727X
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