On a classification of locally 2-Sierpinski spaces (Q2425362)

2-Sierpinski space is a set \(U=\{a, b_1, b_2, c\}\) endowed with the topology \(\{\emptyset, \{a\}, \{a, b_1\}, \{a, b_2\}, U\}\). In this paper, a bijection between topological spaces, locally homeomorphic to the square of Sierpinski space, and graphs without isolated vertices is established. This is used to describe some topological properties of these spaces in combinatorial terms and to disprove a conjecture of \textit{M. Rostami} [Kyungpook Math. J. 37, No.~1, 117--122 (1997; Zbl 0870.54021)] in particular.