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Review (12/20/08)

Prologue. When I was trying to prove the statement given in [Mun00, p.504, l.-9-l.-8], I recognized that the coherent topology given in [Mun00, p.435] is the weak topology given in [Dug, chap. VI, Sec. 8]. After I reviewed part of [Dug, chap. VI], I was able to solve [Mun00, p.186, Exercise 11] because the discussion on the weak topology in [Dug, chap. VI] is more systematic than the discussion on the coherent topology in [Mun00, §71].

After finishing reading a book, one should not read it again
Until one has read another book on the same subject.
Otherwise, the second reading is a repetition rather than a review.
A repetition is nothing but moving backwards.
It is the time when one studies the same subject with a different approach
That one needs a review to compare the various perspectives in detail.
It is the time when one moves forward
That one needs a review to remove obstacles,
To clarify confusions, and to merge a new path with a old one.
If one cannot move forward,
It only means one needs time to digest what one has learned.
Cattle chew, regurgitate, and chew again
To appreciate the taste of grass to the utmost.
One will start again once one overcomes one's fear 1.
A review is not for one to retrieve what one has lost
Or to boast about one's good memory.
A review serves to correct one's misconceptions,
To grasp what one has ignored,
And to animate the old material.
A review serves to gain sight into the big picture
And to elaborate one's mental networks.

1 (12/29/08) After I read (cf. VIII.5) in [Dug, p.336, l.16], I reviewed [Dug, §VIII.5]. After I read (cf. Appendix 1, 4) in [Dug, p.173, l.3], I studied [Dug, Appendix 1]. However, I did not understand the proof of [Dug, p.414, Theorem 2.2]. The failed attack caused anything that is related to the material beyond that theorem in [Dug, Appendix 1] to arouse my lingering fear even if it was a simple concept such as the concept of simplexes. A couple of months later, I simply ignored the statement "(cf. VIII.5)" in [Dug, p.336, l.16]. I discovered that I could advance smoothly without considering Dugundji's references.


1. [Dug] Dugundji, J.: Topology, Boston: Allyn and Bacon, 1966.

2. [Mun00] Munkres J. R.: Topology, 2nd ed., Englewood Cliffs, NJ: Prentice-Hall, 2000.