Commun. Korean Math. Soc. 2013; 28(4): 819-825
Printed October 1, 2013
https://doi.org/10.4134/CKMS.2013.28.4.819
Copyright © The Korean Mathematical Society.
Xinxing Wu and Peiyong Zhu
University of Electronic Science and Technology of China, University of Electronic Science and Technology of China
Similarly to Tychonoff product, we introduce the concept of generalized product topology which is different from the notion of product of generalized topologies in [\'{A}. Cs\'{a}sz\'{a}r, {\it 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, $\alpha$-connect\-ed\-ness, $\sigma$-connectedness, $\pi$-connectedness, $\beta$-connectedness
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