MA651 Topology. Midterm Exam.
Due February 28, 2006 1. Let two positive real functions f1 and f2 on [0, 1] be equivalent if 0 < lim inf
x0
f1 (x) f1 (x) , lim sup < f2 (x) f2 (x) x0
Show that this is an equivalence relation, and that its quotient set is u
MA651 Topology. Questions for quizzes 3.
1. Fundamental family (Definition 19.1) 2. Topology, topological space (Definitions 19.3, 20.1, 20.2) 3. Finer and coarse topologies (Definition 20.4) 4. Theorem of a topology generated by a family of subsets (Theo