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In a previous article , we found the number of ways to run up a staircase with $n$ steps, where there was no restriction on the size $s$ of each step taken, other than $1\leq s\leq n$ ($n\geq 1$). In this paper, we first answer questions posed in , where there are some restrictions on $s$, and then we pose some further questions for the reader.
In this paper we combine the concept of simple extensions of a fuzzy topology with closure structure of fuzzy points to give certain necessary and sufficient conditions for a fuzzy topology to have a cover in the lattice of fuzzy topologies.