Some Topological Properties of The Set of Filter Cluster Functions
Keywords:
F-cluster function, F-limit function, limit functionAbstract
In [1], we generalized the concepts of pointwise convergence, uniform convergence and alpha-convergence for sequences of functions on metric spaces by using the filters on N. Then, in [2], we defined the concepts of limit function, F-limit function and F-cluster function respectively for each of these three types of convergence, where F is a filter on N. In this work, we investigate some topological properties of the sets of F-pointwise cluster functions, F-alpha-cluster functions and F-uniform cluster functions by using pointwise and uniform convergence topologies.References
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