Rarely convergent sequences in topological spaces

Tarkan Öner

Abstract


In this work, by using rare sets, we introduce a new type of convergence in topological spaces, called rare convergence, which is weaker than ordinary convergence. After presenting some examples, we investigate the relationship of rare convergence with continuity and rare continuity. Using rare convergence, we also construct a new topology, called rarely sequential topology, which is coarser than sequential topology.


Keywords


Rare sets; rare continuity; rare convergence; rarely sequential spaces

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References


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