[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2013.28.4.819

GENERALIZED PRODUCT TOPOLOGY

Wu, Xinxing (School of Mathematics University of Electronic Science and Technology of China)
Zhu, Peiyong (School of Mathematics University of Electronic Science and Technology of China)

Publication Information

Communications of the Korean Mathematical Society / v.28, no.4, 2013 , pp. 819-825 More about this Journal

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;

Citations & Related Records

Reference

1	C. Cao, B. Wang, and W. Wang, Generalized topologies, generalized neighborhood systems, and generalized interior operators, Acta Math. Hungar. 132 (2011), no. 4, 310-315. DOI
2	R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
3	R. Shen, A note on generalized connectedness, Acta Math. Hungar. 122 (2009), no. 3, 231-235. DOI
4	R. Shen, Remarks on products of generalized topologies, Acta Math. Hungar. 124 (2009), no. 4, 363-369. DOI
5	A. Csaszar, Generalized open sets, Acta Math. Hungar. 75 (1997), no. 1-2, 65-87. DOI ScienceOn
6	A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351-357. DOI ScienceOn
7	A. Csaszar, ${\gamma}$ -connected sets, Acta Math. Hungar. 101 (2003), no. 4, 273-279. DOI
8	A. Csaszar, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), no. 1-2, 53-66. DOI
9	A. Csaszar, On generalized neighbourhood systems, Acta Math. Hungar. 121 (2008), no. 4, 395-400. DOI
10	A. Csaszar, Modification of generalized topologies via hereditary classes, Acta Math. Hungar. 115 (2007), no. 1-2, 29-36. DOI ScienceOn
11	A. Csaszar, ${\delta}$ - and ${\theta}$ -modifications of generalized topologies, Acta Math. Hungar. 120 (2008), no. 3, 275-279. DOI ScienceOn
12	A. Csaszar, Products of generalized topologies, Acta Math. Hungar. 123 (2009), no. 1-2, 127-132. DOI