Recall that a space $X$ is a c-semistratifiable (CSS) space, if the compact sets of $X$ are $G_{\delta }$-sets in a uniform way. In this note, we introduce another class of spaces, denoting it by k-c-semistratifiable (k-CSS), which generalizes the concept of c-semistratifiable. We discuss some properties of k-c-semistratifiable spaces. We prove that a $T_2$-space $X$ is a k-c-semistratifiable space if and only if $X$ has a $g$ function which satisfies the following conditions: (1) For each $x\in X$, $\left\{x\right\}=\bigcap \left\{g\right(x,n):n\in \mathbb{N}\}$ and $g(x,n+1)\subseteq g(x,n)$ for each...

We study the solutions and attractivity of the difference equation $x_{n+1}=x_{n-3}/(-1+x_n{x}_{n-1}{x}_{n-2}{x}_{n-3})$ for $n=0,1,2,\cdots$ where $x_{-3},x_{-2},x_{-1}$ and $x_0$ are real numbers such that $x_0{x}_{-1}{x}_{-2}{x}_{-3}\ne 1.$

It is shown that a space $X$ is $L\left({}^{\mu }p\right)$-Weakly Fréchet-Urysohn for $p\in {\omega }^{*}$ iff it is $L\left({}^{\nu }p\right)$-Weakly Fréchet-Urysohn for arbitrary $\mu ,\nu <{\omega }_1$, where ${}^{\mu }p$ is the $\mu$-th left power of $p$ and $L\left(q\right)=\{{}^{\mu }q:\mu <{\omega }_1\}$ for $q\in {\omega }^{*}$. We also prove that for $p$-compact spaces, $p$-sequentiality and the property of being a $L\left({}^{\nu }p\right)$-Weakly Fréchet-Urysohn space with $\nu <{\omega }_1$, are equivalent; consequently if $X$ is $p$-compact and $\nu <{\omega }_1$, then $X$ is $p$-sequential iff $X$ is ${}^{\nu }p$-sequential (Boldjiev and Malyhin gave, for each $P$-point $p\in {\omega }^{*}$, an example of a compact space $X_p$ which is ${}^{2}p$-Fréchet-Urysohn...