@article{Zhang2022, 
author = {Xiaoyuan Zhang and Meng Bao and Xiaoquan Xu},
title = {On function spaces related to some kinds of weakly sober spaces},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {9311-9324},
keywords = {bounded sober space, k-bounded sober space, weakly sober space, cut space, function space},
url = {https://www.sciopen.com/article/10.3934/math.2022516},
doi = {10.3934/math.2022516},
abstract = {In this paper, we mainly study function spaces related to some kinds of weakly sober spaces, such as bounded sober spaces,    k-bounded sober spaces and weakly sober spaces. For        T          0       spaces    X and    Y, it is proved that    Y is bounded sober iff the function space              T      o      p        (  X  ,  Y  ) of all continuous functions    f  :  X  ⟶  Y equipped with the pointwise convergence topology is bounded sober iff              T      o      p        (  X  ,  Y  ) equipped with the Isbell topology is bounded sober. But for a    k-bounded sober space    X, the function space              T      o      p        (  X  ,  Y  ) equipped with the pointwise convergence topology or the Isbell topology may not be    k-bounded sober. It is shown that if the function space              T      o      p        (  X  ,  Y  ) equipped with the pointwise convergence topology or the Isbell topology is weakly sober (resp., a cut space), then    Y is weakly sober (resp., a cut space). Relationships among some kinds of (weakly) sober spaces are also investigated.}
}