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Pβ-connectedness in grill topological spaces
Abd El Fattah El Atik,Atef Hussien 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.22 No.1
A grill-$P_{\beta}$-connectedness is more generalization of $P_{\beta}$- connectedness and connectedness and amounting to grill-preconnectedness. The properties of this motif are studied and its relationship with other forms of grill-connectedness. Grill locally preindiscrete spaces are defiened as the spaces in which grill-preopen sets are grill-closed. In these spaces grill connectedness becomes amounting to grill preconnectedness and hence to grill-$P_{\beta}$-connectedness, and grill-semi-connectedness becomes equivalent to grill-$P_{\beta}$-connectedness. The motif of locally grill-$P_{\beta}$-connected space is introduced.