3-sphere two 3-balls. This construction is analogous to a construction of a 2-sphere, performed by gluing the boundaries of a pair of disks. A disk is a 2-ball, and the boundary of a disk is a circle (a 1-sphere). Let a pair of disks be of the same diameter. Superpose them and glue corresponding points on their boundaries. Again one may think of the third dimension as temperature. Likewise, we may inflate the 2-sphere, moving the pair of disks to become the northern and southern hemispheres. After removing a single point from the 2-sphere, what remains is homeomorphic to the Euclidean
What Is a Nation? to the reasons based on race, geography, history and so on. They argue that Renan maintains his intellectual background but subtly, i.e. the arguments he explicitly used in "What is a Nation?" are not consistent with his thinking. The concept of "daily plebiscite" would be ambiguous. They argue that the definition is an opportunist idealization and it should be interpreted within the Franco-Prussian War and in the midst of the dispute concerning the Alsace-Lorraine region. What Is a Nation? "What is a Nation?" ("Qu'est-ce qu'une nation?") is an 1882 lecture by French historian Ernest Renan (1823–1892), known for the statements