MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Semiregular properties and generalized Lindelöf spaces
A. J. Fawakhreh, A. K\i l\i \c cman

Abstract

Let $(X, \tau)$ be a topological space and $(X, \tau^{\ast})$ its semiregularization. Then a topological property ${\Cal P}$ is semiregular provided that $\tau$ has property ${\Cal P}$ if and only if $\tau^{\ast}$ has the same property. In this work we study semiregular property of almost Lindelöf, weakly Lindelöf, nearly regular-Lindelöf, almost regular-Lindelöf and weakly regular-Lindelöf spaces. We prove that all these topological properties, on the contrary of Lindelöf property, are semiregular properties.

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Keywords: Semiregular property, semiregularization topology, nearly Lindelöf, almost Lindelöf, weakly Lindelöf, nearly regular-Lindelöf, almost regular-Lindelöf and weakly regular-Lindelöf spaces.

MSC: 54A05, 54A20, 54F45

Pages:  77--80     

Volume  56 ,  Issue  3$-$4 ,  2004