On the closurepreserving sum theorem
Authors:
M. K. Singal and Shashi Prabha Arya
Journal:
Proc. Amer. Math. Soc. 53 (1975), 518522
MSC:
Primary 54B99
MathSciNet review:
0383335
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Abstract: The closurepreserving sum theorem holds for a property if the following is satisfied: ``if is a hereditarily closurepreserving closed covering of such that each possesses the property , then possesses ". A general technique for proving this theorem is developed. The theorem is shown to hold for a large number of topological properties. As an application, three general sum theorems have also been obtained.
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 C. E. Aull, Paracompact subsets, General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966), Academia, Prague, 1967, pp. 4551. MR 38 #2737. MR 0234420 (38:2737)
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 R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175186. MR 13, 264. MR 0043449 (13:264f)
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 C. J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 116. MR 32 #6409. MR 0188982 (32:6409)
 [4]
 , Stratifiable spaces and continuous extensions, Topology Conf., Arizona State University, Tempe, Ariz., 1967, pp. 3754.
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 D. K. Burke, On subparacompact spaces, Proc. Amer. Math. Soc. 23 (1969), 655663. MR 40 #3508. MR 0250269 (40:3508)
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 G. D. Creede, Semistratifiable spaces, Topology Conf., Arizona State University, Tempe, Ariz., 1967, pp. 318323.
 [7]
 S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107115. MR 31 #5184. MR 0180954 (31:5184)
 [8]
 H. Herrlich, Quotienten geordneter Räume and Folgenkonvergenz, Fund. Math. 61 (1967), 7981. MR 36 #4528. MR 0221476 (36:4528)
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 R. C. Moore and S. G. Mrowka, Topologies determined by countable objects, Notices Amer. Math. Soc. 11 (1964), 554. Abstract #61488.
 [10]
 A. Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1968), 236254. MR 37 #5846. MR 0230283 (37:5846)
 [11]
 M. K. Singal and Shashi Prabha Arya, Two sum theorems for topological spaces, Israel J. Math. 8 (1970), 155158. MR 41 #7612. MR 0263007 (41:7612)
 [12]
 , More sum theorems for topological spaces, Pacific J. Math. 59 (1975). MR 0388332 (52:9169)
 [13]
 , A note on the locally finite sum theorem, Mathematika 19 (1972), 121127. MR 47 #9511. MR 0320978 (47:9511)
 [14]
 M. K. Singal and Pushpa Jain, subparacompact spaces, Jñānabha 2 (1972), 143158. MR 0365484 (51:1736)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197503833356
PII:
S 00029939(1975)03833356
Keywords:
Closurepreserving,
hereditarily closurepreserving,
strongly hereditarily closurepreserving,
locally finite,
hereditarily closurepreserving,
strongly hereditarily closurepreserving
Article copyright:
© Copyright 1975
American Mathematical Society
