• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.549-557
• /
• 2015

We introduce strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces which are stronger than ${\kappa}$-$Fr{\acute{e}}chet$ and ${\kappa}$-net spaces respectively. For convenience, we use the terminology "${\kappa}$-sequential" instead of "${\kappa}$-net space", introduced by R.E. Hodel in [5]. And we study some properties and topological operations on such spaces. We also define strictly ${\kappa}$-$Fr{\acute{e}}chet$ and strictly ${\kappa}$-sequential spaces which are more stronger than strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces respectively.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.669-678
• /
• 2014

We investigate various properties of ${\kappa}$-net convergence structures and define a ${\kappa}$-net-based continuous function on ${\kappa}$-net $\mathcal{L}^+$-convergence structures, and study relationships between continuity and ${\kappa}$-net-based continuity on ${\kappa}$-net $\mathcal{L}^+$-convergence structures. We also provide some characterizations of ${\kappa}$-net-based continuity.