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GENERALIZED PRODUCT TOPOLOGY

Wu, Xinxing;Zhu, Peiyong

  • Received : 2012.11.15
  • Published : 2013.10.31

Abstract

Similarly to Tychonoff product, we introduce the concept of generalized product topology which is different from the notion of product of generalized topologies in [$\acute{A}$. $Cs\acute{a}sz\acute{a}r$, Acta Math. Hungar. 123 (2009), 127-132] for generalized topology and obtain some properties about it. Besides, we prove that connectedness, ${\sigma}$-connectedness and ${\alpha}$-connectedness are all preserved under this product.

Keywords

generalized product topology (GPT);connectedness;${\alpha}$-connectedness;${\sigma}$-connectedness;${\pi}$-connectedness;${\beta}$-connectedness

References

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