Vol. 30, No. 1, 1969

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Sum theorems for topological spaces

Richard Earl Hodel

Vol. 30 (1969), No. 1, 59–65

This paper is a study of Sum Theorems for various classes of topological spaces. Specifically, suppose that X is a topological space and {Fa} is a cover of X such that each Fα belongs to some class Q of topological spaces. When can we assert that X is in Q? We shall concentrate our attention on those cases where the elements of {Fα} are either all open or all closed and the collection {Fα} is a σ-locally finite cover of X.

Mathematical Subject Classification
Primary: 54.50
Received: 16 February 1968
Published: 1 July 1969
Richard Earl Hodel