A correction to the paper: ``Semi-open sets and semi-continuity in topological spaces'' (Amer. Math. Monthly **70** (1963), 36-41) by Norman Levine

Author:
T. R. Hamlett

Journal:
Proc. Amer. Math. Soc. **49** (1975), 458-460

MSC:
Primary 54A10

MathSciNet review:
0367888

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Abstract: A subset of a topological space is said to be semi-open if there exists an open set such that where denotes the closure of . The class of semi-open sets of a given topological space is denoted . In the paper *Semi-open sets and semi-continuity in topological spaces*, Amer. Math. Monthly **70** (1963), 36-41, 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 above-mentioned theorem and its corollary are false. This paper shows how different topologies on a set which determine the same class of semi-open subsets can arise from functions, and points out some of the implications of two topologies being related in this manner.

**[1]**S. Gene Crossley and S. K. Hildebrand,*Semi-closure*, Texas J. Sci.**22**(1971), 99-112.**[2]**-,*Semi-closed sets and semi-continuity in topological spaces*, Texas J. Sci.**22**(1971), 123-126.**[3]**S. Gene Crossley and S. K. Hildebrand,*Semi-topological properties*, Fund. Math.**74**(1972), no. 3, 233–254. MR**0301690****[4]**James Dugundji,*Topology*, Allyn and Bacon, Inc., Boston, Mass., 1966. MR**0193606****[5]**Yoshinori Isomichi,*New concepts in the theory of topological space—supercondensed set, subcondensed set, and condensed set*, Pacific J. Math.**38**(1971), 657–668. MR**0310821****[6]**Norman Levine,*Semi-open sets and semi-continuity in topological spaces*, Amer. Math. Monthly**70**(1963), 36–41. MR**0166752****[7]**Stephen Willard,*General topology*, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR**0264581**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367888-X

Keywords:
Semi-continuous,
semi-correspondent,
semi-open

Article copyright:
© Copyright 1975
American Mathematical Society