A lodgement or lodgment is an enclave, taken and defended by force of arms against determined opposition, made by increasing the size of a bridgehead, beachhead, or airhead[1] into a substantial defended area, at least the rear parts of which are out of direct line of fire.
[2] An example is Operation Overlord, the establishment of a large-scale lodgement in Normandy during World War II.
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