Sphere two poles is called the axis of rotation. Circles on the sphere that are parallel to the equator are lines of latitude. This terminology is also used for such approximately spheroidal astronomical bodies as the planet Earth (see geoid). Any plane that includes the center of a sphere divides it into two equal hemispheres. Any two intersecting planes that include the center of a sphere subdivide the sphere into four lunes or biangles, the vertices of which all coincide with the antipodal points lying on the line of intersection of the planes. The antipodal quotient of the sphere is the
Sphere -ball; thus, it is homeomorphic to the Euclidean -sphere, but perhaps lacking its metric. The -sphere is denoted . It is an example of a compact topological manifold without boundary. A sphere need not be smooth; if it is smooth, it need not be diffeomorphic to the Euclidean sphere. The Heine–Borel theorem implies that a Euclidean -sphere is compact. The sphere is the inverse image of a one-point set under the continuous function . Therefore, the sphere is closed. is also bounded; therefore it is compact. Remarkably, it is possible to turn an ordinary sphere inside out in a three-dimensional