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This paper considers a topological transversality theorem for multivalued maps with continuous, compact selections. Basically, this says, if we have two maps <i>F</i> and <i>G</i> with continuous compact selections and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>F</mi> <mo>&#8773;</mo> <mi>G</mi></mrow></semantics></math></inline-formula>, then one map being essential guarantees the essentiality of the other map.