pg. 3: if A is closed, bar{A}=A. Add note to end of 1-3: in a Hausdorff space, a sequence can only converge to 1 point. pg. 4: Delete the 2nd "i.e...." statement near the end of 1-5. In the definition for completely regular space, f(A)={1}. In the definition for normal, "exists" should be "exist." pg. 5: 2nd line, "converge" should be "converges. Add: The following are normal. *Regular space with countable basis *Metrizable space *Compact Hausdorff space Add: if Y is compact in Hausdorff X, x_0\nin Y, there are disjoint open sets U,V of X containing x_0,Y. Add: A countable product of 1st-countable spaces is 1st-countable. pg. 6: Delete last sentence of 1-10. Add: If H is normal then G/H is a topological group. pg. 7: Arrowa A->B means B is subset of A. Add the following arrows: compactly generated -> 1st axiom countability 1st axiom countability -> 2nd axiom countability Lindelof -> compact Baire space -> complete metric space Connected -> path connected Delete the following arrows: Locally connected -> connected Locally path connected -> path connected Baire space -> metric space Delete "a finite subcover" from countably compact. Centered means the intersection of a finite number of sets in the system is nonempty. Delete "countable" from compact. For completely regular space, replace "f(A)={0}" with "f(B)=1". Add to connected: "Equivalently, no separation (open proper subsets A and B such that AUB=X.) Add "Hausdorff" to hypothesis of Smirnov. Add: In a metric space, Lindelof=separable=2nd countable pg. 8 Delete last statement in 1st paragraph. Extreme Value Theorem: change "f is compact" to "f is continuous" pg. 9 compact subspace C of x (not X). In existence part of proof, *Delete "C" at end of period. *add X-C (not add C) *Replace "Y is compact" with "Y is Hausdorff" Converse is proof that X is locally compact. For part 2 of Stone-Cech, note: If h:X->Z is an imbedding where Z is compact Hausdorff, there is a compactiication Y of X as h extends to an imbedding H:Y->, unique up to equivalence. pg.10 2-5 note open refinement is defined in 3-6. pg. 11 Last statement of 3-1: switch d, d' 3-2 Add the following: Lebesgue number lemma: If A is an open cover of (X,d) and X is compact, then there exists delta>0 such that for each subset of X with diameter Finer. When J is infinite, R^J is not metrizable in product or box topology. p.12 In Urysohn, replace regular space with normal space. p.13 Let X be a regular space with countably locally finite base B. p.15 Item 2: both open and closed. Delete "Cartesian" in item 5 of basic results. IVT: Replace "c is between" with "r is between" p.16 Proof of existence: replace \phi_i with \phi_j.