A correction to the paper: ``Semiopen sets and semicontinuity in topological spaces'' (Amer. Math. Monthly 70 (1963), 3641) by Norman Levine
Author:
T. R. Hamlett
Journal:
Proc. Amer. Math. Soc. 49 (1975), 458460
MSC:
Primary 54A10
MathSciNet review:
0367888
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Abstract: A subset of a topological space is said to be semiopen if there exists an open set such that where denotes the closure of . The class of semiopen sets of a given topological space is denoted . In the paper Semiopen sets and semicontinuity in topological spaces, Amer. Math. Monthly 70 (1963), 3641, Norman Levine states in Theorem 10 that if and are two topologies for a set such that , then . In a corollary to this theorem, Levine states that if , then . An example is given which shows the abovementioned theorem and its corollary are false. This paper shows how different topologies on a set which determine the same class of semiopen subsets can arise from functions, and points out some of the implications of two topologies being related in this manner.
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 S. Gene Crossley and S. K. Hildebrand, Semiclosure, Texas J. Sci. 22 (1971), 99112.
 [2]
 , Semiclosed sets and semicontinuity in topological spaces, Texas J. Sci. 22 (1971), 123126.
 [3]
 , Semitopological properties, Fund. Math. 74 (197 2), 233254. MR 46 #846. MR 0301690 (46:846)
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 J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
 [5]
 Y. Isomichi, New concepts in the theory of topological spacesupercondensed set, subcondensed set, and condensed set, Pacific J. Math. 38 (1971), 657668. MR 46 #9919. MR 0310821 (46:9919)
 [6]
 Norman Levine, Semiopen sets and semicontinuity in topological spaces, Amer. Math. Monthly 70 (1963), 3641. MR 29 #4025. MR 0166752 (29:4025)
 [7]
 Stephen Willard, General topology, AddisonWesley, Reading, Mass., 1970. MR 41 #9173. MR 0264581 (41:9173)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919750367888X
PII:
S 00029939(1975)0367888X
Keywords:
Semicontinuous,
semicorrespondent,
semiopen
Article copyright:
© Copyright 1975
American Mathematical Society
