Ian Stares
Decreasing (G) spaces

Comment.Math.Univ.Carolinae 39,4 (1998) 809-817.

Abstract: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.

Keywords: decreasing (G), decreasing (A), homogeneous, monotone normality, closed map
AMS Subject Classification: 54E20, 54D70, 54C10

PDF