Sung-Hoon Park - Quotient Topology
... Let p: X Y be a quotient map. Let Z be a space and let g: X Z be a map that is constant on each set p1(y), for y Y. then g induces a map f: Y Z such that f g=g. The induced map f is continuous if and only if g is continuous; f is a quotient map if and only if g is a quotient map. ...
... Let p: X Y be a quotient map. Let Z be a space and let g: X Z be a map that is constant on each set p1(y), for y Y. then g induces a map f: Y Z such that f g=g. The induced map f is continuous if and only if g is continuous; f is a quotient map if and only if g is a quotient map. ...
Document
... M and Q, P and N. Sample answer: P is supplementary to M and Q, therefore by the Congruent Supplements Theorem they are congruent; Q is supplementary to P and N, therefore by the Congruent Supplements Theorem they are congruent. ...
... M and Q, P and N. Sample answer: P is supplementary to M and Q, therefore by the Congruent Supplements Theorem they are congruent; Q is supplementary to P and N, therefore by the Congruent Supplements Theorem they are congruent. ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.