@article{Xie2022, 
author = {Xiaolin Xie and Hui Kou},
title = {The Cartesian closedness of c-spaces},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {16315-16327},
keywords = {dcpo, domain, directed spaces, continuous spaces, monotone determined spaces, c-spaces},
url = {https://www.sciopen.com/article/10.3934/math.2022891},
doi = {10.3934/math.2022891},
abstract = {Directed space was defined by Hui Kou in 2014 [21], which is equivalent to        T    0   monotone determined space. Its main purpose is to build an extended framework for domain theory. In this paper, we study the category of c-spaces which is a subcategory of directed spaces. The main results are: (1) we will describe c-spaces using a new definition, which give us the convenience to construct new classes of spaces; (2) we give some conditions such that categorical products and topological products agree in        D    t    o    p  ; (3) the category of c-spaces is not Cartesian closed; (4) we define a new class of spaces, namely, FS-spaces, which forms a Cartesian closed category.}
}