Comments and Errata: Elementary Topology

Here is a list of comments and errata for Elementary Topology (First Edition). Technical errata appear in small type.

This list was last updated Wednesday, November 3, 1999 at 15:55.

• Page xv, line -9. "won" should be own
• Page xii, In section title. "Euclidian" should read "Euclidean".
• Page xviii. Web address lacks tilde, should read: "http://www.math.uiowa.edu/~roseman"
• Page 24 line -12 "open subset of X" should read "open subsets of X"
• Page 26 Definition should add ", with A a non-empty set"
• Page 26 line -8 should read ``Any subset X of R^n''
• Page 31, line 22. "finites" should read "finite".
• Page 41 Problem 1.8 should read "If X is a subset of R^n, then any one point subset is a closed subset of X"
• Page 48, Line -5. In the formula, one too many parentheses after the "q".
• Page 52, Lines 8 and 11. Change "m x n" to "n x m".
• Page 55 line 6 omit black diamond symbol at end of line
• Page 56 omit "counter-clockwise"
• Page 57, Second paragraph both instances of "epsilon-delta" should be "epsilon"
• Page 55 First line fourth paragraph in the notation for set H, there is missing ":"
• Page 58 Proposition 2.37. It might be helpful to note that the sets H_i are nested. Thus the intersection of the first k sets is in fact H_k.
• Page 71 Problem 2.14, belongs in the problem list for Chapter 2.
• Page 71 Problem 2.16 should read: "You might want to look at Example 1.28
• Page 77. Proposition 3.08. The capital "F" should be lower case "f".
• Page 78 Last two lines of Definition 3.11, the capital "F" should be a small "f".
• Page 83, Proposition 3.29. The capital "F" should be lower case "f".
• Page 86, first line of Example 3.38, second to last word should be "which".
• Page 94, line 3. The capital "F" should be lower case "f".
• Page 94,line 19. Omit the L with slash after "torus".
• Page 98. Problem 3.24 should read: Show that f is continuous only at 0 and 1.
• Page 119, Statement of Proposition 4.39. Omit black rectangle at end of statement.
• Page 122, line -8. COMMENT: We could also argue that [0,1] has the fixed property and [0,1) does not.
• Page 127, Problem 4.1, should read: Prove Proposition 4.03.
• Page 127, Problem 4.5. D^2 with circle above it is the open unit disk.
• Page 129, Problem 4.36, should read: Prove Proposition 4.42.
• Page 129, Problem 4.40. Add the hypothesis that X and Y are homeomorphic.
• Page 133, line -16. Formula should read f(x) = 3x -2.
• Page 137, line -9. Should read, " intersection of the A_i", not C_i.
• Page 140, top two lines. Should read: In each place of p, we change the 0 to a 2 and a 2 to a 0 if x and y disagree in that place, otherwise, make no change. The result is f(p).
• Page 160, Problem 5.3. See comment for page 414 below, for a detail of the explicit definition of the map. Hints: it might help to express continuity via sequences. Also, you might focus on points expressed using a terminal sequence of 2s.
• Page 160, Problem 5.12. Should read X' and K are homeomorphic.
• Page 160, Problem 5.15. Example 5.3 should be Example 5.20, and Q should be K^2.
• Page 180-181. In Exercises 6.22 and 6.22, as well as caption for Figure 6-10 formulas should have the second cos as sin, and thus read: f(t) = ( e^t cos(t), e^t sin(t) ).
• Page 191, lines -10 and -9. Formula should read ad -bc.
• Page 191, line -9. The L with slash should be space and thus read should read "set of".
• Page 193, line 14. "x = 2 |y|" should read "y = 2 |x|", as shown in Figure 7-5. Note that, since diagonal lines have slope of +2 and -2, the vertical line segments cannot intersect these lines. (Using x = 2 |y|, the origin would be cut point of order 5 (if C₁ = B₁) or 6(if C₁ = A₁), and rest of argument should be OK.)
• Page 193, line -6. Misplaced period at beginning of line.
• Page 197, line 3. Proposition should begin with capital.
• Page 197, Problem.7.10 Misplaced period at beginning of last line.
• Page 197, Problem 7.12 "complement" not "compliment".
• Page 236, Caption for Figure 10-1. omit initial "(" in the formula.
• Page 316, Figure 14-9. Graphic is not clear enough to see exactly what the small knot is. We will soon add some interactive graphics to our web site to clarify.
• Page 326, Definition 15.01. "there is continuous" should read ""there is a continuous"".
• Page 327 line -5, should read "a simple" not "an simple".
• Page 330, Proposition 15.14 "If X and Y" should read "Then X and Y"
• Page 330, line 9 "connection between" rather than "connection to" .
• Page 331, line 9. "deform" should read "deforms".
• Page 331, line 13. "during" should read "during".
• Page 333 line -4. Formula for g with tilde should be "-Pi t" instead of "Pi t",
• Page 333, line -2. "not all" should read "is not all".
• Page 336, line 8. "Siefert" should read "Seifert".
• Page 338, line -15. "en" should read "e".
• Page 339, line -12. Omit ",to the abstract setting".
• Page 339, line -10. "::" should read ":".
• Page 340, Definition 15.47. add colon between phi_* and \pi_1.
• Page 340, Proposition 15.48, second to last line. "with deformation" should read "with retraction".
• Page 341, line 4. the L with slash should be removed leaving "then" .
• Page 414,Line 6.COMMENT: With regard to problem 5.3, we should be explicit on this adjustment. The correspondence would begin: