Generalized product topology
Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 819-825
Printed October 1, 2013
Xinxing Wu and Peiyong Zhu
University of Electronic Science and Technology of China, University of Electronic Science and Technology of China
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 [\'{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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