Abstract
<abstract><p>Directed space was defined by Hui Kou in 2014 <sup>[<xref ref-type="bibr" rid="b21">21</xref>]</sup>, 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 $ {\bf Dtop} $; (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.</p></abstract>
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