On slight homogeneous and countable dense homogeneous spaces

Samer Al Ghour, Nahed Al Khatib

As two separated concepts connectedness and homogeneity are generalized by slight homogeneity. Sum theorems and product theorems regarding slight homogeneous spaces are obtained. Many results concerning slight homogeneous components are given. Also, SCDH spaces generalize CDH spaces. It is proved in an extremally disconnected SCDH space that, all slightly homogenous components are clopen and SCDH subspaces. Many other results and many examples and counter-examples concerning slight homogeneity and SCDH spaces are obtained.