In the class of Alexandroff spaces we study the properties of being a submaximal, door, Whyburn and weakly Whyburn space. We provide characterizations in order theoretical terms. Connections with posets, counting formulas and numerical results in the class of finite spaces are also given.
Alexandroff space, submaximal space, door space, Whyburn space
LAZAAR, SAMI; SABRI, HOUSSEM; and TAHRI, RANDA
"On some topological properties in the class of Alexandroff spaces,"
Turkish Journal of Mathematics: Vol. 45:
1, Article 29.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/29