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.
