Extensions of Pontryagin duality

@article{Venkataraman1975ExtensionsOP,
  title={Extensions of Pontryagin duality},
  author={R. Venkataraman},
  journal={Mathematische Zeitschrift},
  year={1975},
  volume={143},
  pages={105-112}
}
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References

SHOWING 1-6 OF 6 REFERENCES
$k$-groups and duality
Recall that a function is Ac-continuous if its restriction to each compact subset of its domain is continuous. We call a topological group G a Ac-group if each ¿-continuous homomorphism on G isExpand
Dualität lokalkompakter Gruppen
Dualität Iokalkompakter Gruppen