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
Public sphere pedagogy sphere pedagogy might alienate students and community members unaccustomed to this type of dialectic experience. In addition to its exclusionary nature, attention has also been called to Habermas' privileging of a hegemonic public sphere. Michael Warner argues that the bourgeois public sphere was structured to be affable to those privileged few who made up the powerful upperclass. While students participating in public sphere pedagogy application receive special training in their classrooms, the same is not necessarily true of community members who participate. This specialized student training draws two critiques. First, conceiving of public pedagogy as a form of instruction risks