• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.251-256
• /
• 2010

In this paper, we introduce the notions of ${\alpha}m$-open sets and ${\alpha}M$-continuous functions and investigate some properties of such concepts.

• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.117-121
• /
• 1999

In this paper, we introduce $m$-open(closed) mappings by $m$-sets, and obtain a number of their properties. In particular, $m$-open(closed) mappings are used to extend known results for ${\alpha}$-open mapping, semi-open mappings and preopen mappings.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.603-611
• /
• 2012

We introduce the concept of fuzzy $r$-minimal ${\alpha}$-open set on a fuzzy minimal space and some basic properties. We also introduce the concepts of fuzzy $r$-M ${\alpha}$-continuous and fuzzy $r$-M($M^*$) ${\alpha}$-open mappings, and investigate characterization for such mappings.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.1
• /
• pp.54-58
• /
• 2010

We introduce the concepts of interval-valued fuzzy $m{\alpha}$-open sets and interval-valued fuzzy $m{\alpha}$-continuous mappings. And we study some characterizations and properties of such concepts.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.2
• /
• pp.83-93
• /
• 2009

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy $\alpha$-I-open and r-fuzzy $\beta$-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy $\alpha$-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal $\alpha$-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.

• Kyungpook Mathematical Journal
• /
• v.32 no.1
• /
• pp.21-30
• /
• 1992

• Honam Mathematical Journal
• /
• v.31 no.1
• /
• pp.31-43
• /
• 2009

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF m-precontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.1
• /
• pp.1-6
• /
• 2010

The notion of $\star$-Externally disconnected fuzzy ideal topological spaces is introduced and studied. Many characterizations of the space are obtained.

• Kyungpook Mathematical Journal
• /
• v.54 no.3
• /
• pp.387-399
• /
• 2014

We show that in quasi-topological spaces, separation axiom $T_2$ is equivalent to ${\alpha}-T_2$, $T_0$ is equivalent to semi - $T_0$, and semi - $T_{\frac{1}{2}}$ is equivalent to semi - $T_D$. Also, we give characterizations for ${\alpha}-T_1$, semi - $T_1$ and semi - $T_{\frac{1}{2}}$ generalized topological spaces.

• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.635-646
• /
• 2024

In this research work, we introduce and investigate four innovative types of soft spaces, pushing the boundaries of traditional spatial concepts. These new types of soft spaces are named as soft T_b space, soft T^#_b space, soft T^##_b space and soft_αT^#_b space. Through rigorous analysis and experimentation, we uncover and propose distinct characteristics that define and differentiate these spaces. In this research work, we have established that every soft $T_{\frac{1}{2}}$ space is a soft _αT^#_b space, every soft T_b space is a soft _αT^#_b space, every soft T^#_b space is a soft _αT^#_b space, every soft T_b space is a soft T^#_b space, every soft T^#_b space is a soft T^##_b space, every soft $T_{\frac{1}{2}}$ space is a soft ^#T_b space and every soft T_b space is a soft #T_b space.