Example 2 in Chapter 5 of [1] constructs, for an arbitrary closed subset of the real line, a sequence whose set of limit points is exactly the original closed set. We use a similar construction to show that an arbitrary nonempty closed set in a separable metric space is always the set of limit points of some sequence. We note further that if all nonempty closed subsets of a metric space can be realized as sets of limit points of sequences, then that metric space is separable.

A universal twist $\gamma$ for all finite-dimensional Cayley-Dickson algebras is defined recursively and a tree diagram 'computer' is presented for determining the value of $\gamma (p,q)$ for any two non-negative integers $p$ and $q$.

The idea of CC-metric is introduced by Krause [4] and improved by Chen [1]. Later, CC-analogues of some of the topics that include the concept of CC-distance have been studied. In this work, we give the Chinese Checker version of Heron's Formula.

A generalization of the notion of connectedness of subsets in a topological space is given. Several properties of this type of subsets (also those being similar to fundamental results of the theory of connected subsets) are obtained.

We classify by elementary methods the $p$-colorability of torus knots, and prove that every $p$-colorable torus knot has exactly one nontrivial $p$-coloring class. As a consequence, we note that the two-fold branched cyclic cover of a torus knot complement has cyclic first homology group.

In this paper we provide a proof of the algebraic case of a conjecture of Nakanishi concerning a proposed unknotting operation. Specifically, we show, using only basic knot theory techniques, that any algebraic knot or link can be unknotted by a sequence of so-called (2,2)-moves.

In this work, we investigate the Diophantine equation $lx^3-kx^2+kx-l = y^2$ where $k$ and $l$ are positive integers. The two results are Theorems 1.1 and 1.2. The first theorem states that if $k=3l-1$ and $l = \rho^2$, the above equation has a unique integer solution, namely $(x,y) = (1,0)$. The second theorem says that if $k=3l+1$ and $l\equiv 0,1,4,5,7 \pmod 8$ the above equation also has a unique solution, the pair $(x,y) = (1,0)$.