Selection principles in relator spaces

Abstract

Recently, Ko£inac introduced selection principles and games in relator spaces and suggested a systematic study in this area. In this paper we will present some basic results considering the relator Menger and relator Hurewicz properties following some ideas from [12].

On weaker forms of relator Menger, relator Rothberger and relator Hurewicz properties

“…In [12] we defined the corresponding notions in relator spaces: A relator space (X, R) is relator compact (resp., relator Lindelöf ), briefly RC (resp., RL) if for every relation R from R there exists a finite (resp., countable) subset A of X such that R(A) = X. We say that a relator space (X, R) is σ-relator compact (σ-RC) if X is the countable union of relator compact spaces.…”

“…In this paper we continue the investigation of selection principles in relator spaces started in [12]. In the second section we follow the idea of Bonanzinga, Cammaroto, Kočinac and Matveev (see [1]) who used neighbourhoods of sets to define selection principles which are weaker than the known properties of Menger, Rothberger and Hurewicz.…”

“…In the second section we follow the idea of Bonanzinga, Cammaroto, Kočinac and Matveev (see [1]) who used neighbourhoods of sets to define selection principles which are weaker than the known properties of Menger, Rothberger and Hurewicz. In the third section as a motivation we used the papers [12,20], where weaker properties than Menger were defined by closures of sets.…”