On weaker forms of Menger, Rothberger and Hurewicz properties

M. Bonanzinga, F. Cammaroto, Lj. D. R. Końćinac, M. V. Matveev

We introduce new star selection principles defined by neighbourhoods and stars which are weaker versions of the of Menger, Rothberger and Hurewicz properties; in particular the properties introduced are between strong star versions and star versions of the corresponding properties defined in [12]. Some properties of these neighbourhood star selection principles are proved and some examples are given.