Communications of the
Korean Mathematical Society CKMS

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