Compositions of continuous functions and connected functions

Kellum, Kenneth R.; Rosen, Harvey

doi:10.1090/S0002-9939-1992-1073528-7

Compositions of continuous functions and connected functions
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by Kenneth R. Kellum and Harvey Rosen PDF

Proc. Amer. Math. Soc. 115 (1992), 145-149 Request permission

Abstract:

Suppose $f:X \to Y$ is continuous and onto and $g:Y \to Z$ is such that $g \circ f:X \to Z$ has a property we are interested in. For which properties of functions can we infer that $g$ has the same property? Properties for which we can infer this include continuity and the Darboux property. Properties for which we cannot include almost continuity.

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