On the Order Hereditary Closure Preserving Sum Theorem

Jianhua Gong, Ivan L. Reilly
DOI: https://doi.org/10.4995/agt.2007.1892

Abstract

The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem:

(1) If a topological property P satisfies (Σ') and is closed hereditary, and if V is an order hereditary closure preserving open cover of X and each V ϵ V is elementary and possesses P, then X possesses P.

(2) Let a topological property P satisfy (Σ') and (β), and be closed hereditary. Let X be a topological space which possesses P. If every open subset G of X can be written as an order hereditary closure preserving (in G) collection of elementary sets, then every subset of X possesses P.


Keywords

Elementary set; Order hereditary closure preserving; sum theorem

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References

S. P. Arya and M. K. Singal, More sum theorems for topological spaces, Pacific J. Math. 59 (1975), 1-7. http://dx.doi.org/10.2140/pjm.1975.59.1

S. P. Arya and M. K. Singal, On the closure preserving sum theorem, Proc. Amer. Math. Soc. 53 (1975), 518-522. http://dx.doi.org/10.1090/S0002-9939-1975-0383335-6

C. H. Dowker, Inductive-dimension of completely normal spaces, Quart. J. Math. 59 (1975) 1-7.

G. Gao, On the closure preserving sum theorems, Acta Math. Sinica 29 (1986), 58-62.

R. E. Hodel, Sum theorems for topological spaces, Pacific J. Math. 30 (1969), 59-65. http://dx.doi.org/10.2140/pjm.1969.30.59

Y. Katuta, A theorem On paracompactness of product spaces, Proc. Japan. Acad. 43 (1967), 615-618. http://dx.doi.org/10.3792/pja/1195521519

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Universitat Politècnica de València

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