1. Under these identifications, is the inclusion map from to. 2. Inclusion maps in geometry come in different kinds : for example embeddings of submanifolds. 3. This is done in the following way : Let \ iota be the inclusion map: 4. If the inclusion map ( identity function) 5. A case of special interest is when H is a Lie subgroup of G and \ psi is the inclusion map. 6. There is an exotic inclusion map as a transitive subgroup; the obvious inclusion map fixes a point and thus is not transitive. 7. There is an exotic inclusion map as a transitive subgroup; the obvious inclusion map fixes a point and thus is not transitive. 8. Conversely, if " S " is an embedded submanifold which is also a closed subset then the inclusion map is closed. 9. Openness is essential here : the inclusion map of a non-open subset of " Y " never yields a local homeomorphism. 10. This implies that any cofibration can be treated as an inclusion map, and therefore it can be treated as having the homotopy extension property.