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Keywords:
mixed construction; generalized topology; generalized topological space; weak generalized topology; countable subcover; $\mu _{12}^{C}$-open set; $\mu _{C}$-open set; $\mu _{\ast }^{C}$-open set; countable set
mixed construction; generalized topology; generalized topological space; weak generalized topology; countable subcover; $\mu _{12}^{C}$-open set; $\mu _{C}$-open set; $\mu _{\ast }^{C}$-open set; countable set
Summary:
The theory of generalized topologies was introduced by Á. Császár (2002). In the literature, some authors have introduced and studied generalized topologies and some generalized topologies via generalized topological spaces due to Á. Császár. Also, the notions of mixed constructions based on two generalized topologies were introduced and investigated by Á. Császár (2009). The main aim of this paper is to introduce and study further new generalized topologies called $\mu _{12}^{C}$ via mixed constructions based on two generalized topologies $\mu _{1}$ and $\mu _{2}$ on a nonempty set $X$ and also generalized topologies called $\mu _{C}$ and $\mu _{\ast }^{C}$ for a generalized topological space $(X,\mu )$.
References:
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