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math.GN2026
Kernel retracts of co-sober spaces
Xiaoquan Xu, Fengshuo Xu, Haitao Ji +1
Kernel retracts of co-sober spaces need not be co-sober, even when the ambient space is countably infinite and compact. We construct a co-sober -space and a continuous ide…
math.GN2026
On fuzzy contractions in fuzzy metric spaces
Fengshuo Xu, Haitao Ji, Dong Qiu
The classical Banach principle relies on contractive sequences being Cauchy. Gregori and Sapena (2002) established a fuzzy analogue but required this as an extra hypothesis, leavin…
math.GN2026
Smyth power space of a co-sober space is not always co-sober
Xiaoquan Xu, Fengshuo Xu, Haitao Ji +1
In this paper, we give a co-sober space whose Smyth power space is not co-sober, which gives a negative answer to an open problem.