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Keywords:
decreasing (G); decreasing (A); homogeneous; monotone normality; closed map
decreasing (G); decreasing (A); homogeneous; monotone normality; closed map
Summary:
We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown.
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