Problem 3.24. Let X = [0, 1] U{2} C R. On the one hand, X has a subspace topology T1 induced by the standard (order) topology on R. On the other hand, X has a natural order induced by the natural order on R. This order induces an order topology T2 on X. (1) How are T1 and T2 related? (2) Is 1 a limit point of X? (3) Is 2 a limit point of X ? %3D
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Solve 3.24 all the parts in detail please
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J. C. MAYER
Problem 3.24. Let X = [0, 1] U{2} C R. On the one hand, X has a subspace topology Ti
induced by the standard (order) topology on R. On the other hand, X has a natural order
induced by the natural order on R. This order induces an order topology T2 on X. (1) How
are Ti and T2 related? (2) Is 1 a limit point of X? (3) Is 2 a limit point of X?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53e9ab80-64ca-4d50-9be9-589e5309635d%2F039182b4-cdf1-460b-9ee7-232c75a3827b%2Fbcwsd4n_processed.jpeg&w=3840&q=75)
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