Vol. 59, No. 1, 1975

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More sum theorems for topological spaces

Shashi Prabha Arya and M. K. Singal

Vol. 59 (1975), No. 1, 1–7

By a sum theorem for topological spaces is meant a theorem of the following type: If is a cover of a space X, each element of which possesses a property 𝒫, then X also possesses the property 𝒫. Different types of sum theorems for various classes of topological spaces have been obtained from time to time by various authors. Perhaps the simplest known sum theorem is the locally finite sum theorem which states the following: If {Fα;α Λ} be a locally finite closed covering of a space X such that each Fα possesses a property 𝒫, then X possesses 𝒫 The locally finite sum theorem is shown to hold for a large number of important topological properties.

Mathematical Subject Classification 2000
Primary: 54D20
Received: 22 May 1973
Revised: 26 April 1975
Published: 1 July 1975
Shashi Prabha Arya
M. K. Singal