Vol. 90, No. 1, 1980

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On the locally countable sum theorem

Shashi Prabha Arya and M. K. Singal

Vol. 90 (1980), No. 1, 1–10

We say that the locally countable sum theorem holds for a property 𝒫 if whenever {Fα : α Λ} is a locally countable closed covering of X such that each Fα has 𝒫, then X has 𝒫. We prove some general theorems which establish the locally countable sum theorem for properties satisfying certain conditions. It is then shown that a number of sum theorems hold for those properties which are closed hereditary and for which the locally countable sum theorem holds. We apply our theorems to some particular cases to obtain many new results and also to improve upon some known results.

Mathematical Subject Classification
Primary: 54D18, 54D18
Received: 21 November 1978
Revised: 28 September 1979
Published: 1 September 1980
Shashi Prabha Arya
M. K. Singal