5 papers
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…
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…
A note on definable endomorphisms of ordered abelian groups
Haitao Ji, Fengshuo Xu, Dong Qiu
We answer Kourovka Notebook Problem~18.16 affirmatively in the pure language of ordered abelian groups, with parameters allowed. The piecewise-affine description of definable funct…
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.
Classification of maximally non-self-dual modular categories of small dimension
Fengshuo Xu, Jingcheng Dong
We prove that a non-pointed maximally non-self-dual (MNSD) modular category of Frobenius-Perron (FP) dimension less than has at most two possible types, and all these types…