Geodesic
Locally Precompact Groups: (Local) Realcompactness and Connectedness
William W. Comfort1 ; Gábor Lukács2
1Dept. of Mathematics, Wesleyan University, Middletown, CT 06459, U.S.A.
2Dept. of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
Journal of Lie Theory, Tome 20 (2010) no. 2, pp. 347-374

Voir la notice de l'article provenant de la source Heldermann Verlag

A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called "locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties:
(1) Dieudonné completeness; (2) local realcompactness; (3) realcompactness; (4) hereditary realcompactness; (5) connectedness; (6) local connectedness; (7) zero-dimensionality.
They also prove that an abelian locally precompact group occurs as the quasi-component of a topological group if and only if it is "precompactly generated", that is, it is generated algebraically by a precompact subset.
Classification : 22A05, 54H11, 22B05, 22C05
Mots-clés : Precompact group, precompactly generated group, locally precompact group, Weil completion, Dieudonné complete group, locally Dieudonné complete group, realcompact group, locally realcompact group, connected group, locally connected group, omega-balanced g

William W. Comfort  1   ; Gábor Lukács  2

1 Dept. of Mathematics, Wesleyan University, Middletown, CT 06459, U.S.A.
2 Dept. of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada 
William W. Comfort; Gábor Lukács. Locally Precompact Groups: (Local) Realcompactness and Connectedness. Journal of Lie Theory, Tome 20 (2010) no. 2, pp. 347-374. http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a6/
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     title = {Locally {Precompact} {Groups:} {(Local)} {Realcompactness} and {Connectedness}},
     journal = {Journal of Lie Theory},
     pages = {347--374},
     year = {2010},
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