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Bigeneralized topology was introduced in 2010. In this paper, we aim to contribute in the development of this area by proving results with respect to the hereditary class that defines two types of Lindelöf spaces in a bigeneralized topological space (BGTS). Some results on strong BGTS (briefly SBGTS) are proved by defining a -perfect mapping. We also prove some equivalent conditions with respect to the hereditary class. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the research results of DAD, Daily Artificial Dispatcher, published in 2010 [S. Z. Stefanov, New Mathematics and Natural Computation6 (2010) 275–283], and give it new interpretation bring out the best of its meaning, as well as some more quantitative novel formula. In metaphorical sense, DAD is the analogue to DNA and hence the Smart Grid is analogue to the Creature by invoking the postmodern theory [J.-F. Lyotard, Moralités Postmodernes (Éditions Galilée, 1993) (in French)]. Specifically, the DAD’s binary expressions are generated by an innocent dialogue between DAD and Smart Grid in the form of world-strings. Namely, the living space-time of the DAD’s binary symbols is generated via a discussion between DAD and Smart Grid. Metaphorically speaking, DAD’s world is digitally described as a dramatic game and the Smart Grid as a creating cartoon loaded with an integral holographic complexity. Overall, the so called creatures capable of innocent discussions under near-zero temperature are generated by the epidemic growth of the Smart Grid cartoon. It is further concluded that the number of the Smart Grid creatures is inversely proportional to the half-time of the DAD’s binary “DNA” life cycle. Each Smart Grid can be coded in one of eight colors pool, as an aging in one of the four ways and as being in one of three possible development phases, dynamically. Finally, we take the liberty of calling the DAD’s world, a string prescribed as topology and landscape, to be “Aria”. [ABSTRACT FROM AUTHOR]