ASAreeyuth Sama-Ae

Areeyuth Sama-Ae

Prince of Songkla University
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Areeyuth Sama-Ae has a total of 22 co-authors. Here are the top co-authors by number of shared publications:

Latest Publications

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    Semi-θ-Continuous and Semi-θ-Open Multifunctions in Bitopological Spaces: Characterizations, Duality, and Topological Invariance

    by Chawalit Boonpok, Areeyuth Sama-Ae

    In this paper, we introduce and systematically investigate upper and lower semi-θ-continuous multifunctions and semi-θ-open multifunctions in the setting of bitopological spaces. The central concept underlying our approach is that of semi-ϕθ-open sets, defined via the θ-closure and θ-interior operators associated with the two topologies. We establish pointwise and global characterizations of upper semi-θ-continuity in terms of the semi-θ-interior and semi-θ-closure operators together with the upper and lower inverse mappings. Analogous characterizations are obtained for lower semi-θ-continuity, and we demonstrate through explicit examples that upper and lower semi-θ-continuity are independent notions, neither implying the other. We then introduce the dual concept of semi-θ-open multifunctions and derive several equivalent global characterizations, including the analogue of the classical result that a function is open precisely when the image of every open set is open. The interplay between upper semi-θ-continuity and semi-θ-openness is examined: the two notions are shown to be independent for multifunctions, while for bijective single-valued functions they coincide via the inverse mapping. Finally, we extend classical compactness, connectedness, and Hausdorffness to the semi-θ setting, establish their preservation and reflection properties under the relevant classes of multifunctions, and show via counterexamples that the multifunction analogues of certain single-valued results fail in the absence of disjoint-valuedness. The results unify and extend several known characterizations in the literature.

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    Submaximality, Connectedness, and δβI-Continuous Mappings in Ideal Spaces

    by Chawalit Boonpok, Areeyuth Sama-Ae

    This paper extends the concepts of submaximality, connectedness, and hyperconnectedness to ideal topological spaces by means of δβI-open sets, which constitute a class of generalized open sets. Initially, we establish a collection of equivalent conditions that define the δβI-submaximality of an ideal topological space (T, τ, I). This study then discusses δβI-connectedness, which is a more general form of classical connectedness. We demonstrate that some mappings preserve this form of relationship. Finally, we introduce a generalization of hyperconnectedness based on δβI-open sets and provide characterizations of these spaces. These findings jointly augment the theory of ideal topological spaces by establishing coherent frameworks for submaximality, connectedness, and hyperconnectedness while expanding their applicability to more expansive topological situations where conventional separation axioms and continuity ideas are insufficient.

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    Generalized submaximality and paracompactness in ideal topological spaces via δβ*-𝔍-open sets

    by Chawalit Boonpok, Areeyuth Sama-Ae

    This paper explores the notions of δβ*-𝔍-submaximality and δβ*-𝔍-paracompactness within ideal topological spaces, viewing them as natural generalizations of the traditional concepts of submaximality and paracompactness. These concepts arise naturally in the context of ideal topology, where an ideal 𝔍 on a topological space provides additional structure for analyzing topological properties. It focuses on the study of submaximal spaces by employing δβ*-𝔍-open sets, which serve as fundamental building blocks for understanding the topological behavior in ideal spaces. Furthermore, the work provides multiple characterizations of δβ*-𝔍-paracompact spaces and examines how this property behaves under various types of mappings. The results establish important connections between classical topological properties and their ideal counterparts, contributing to the growing theory of ideal topological spaces.

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    Spherical Curves and Their Rigidity in Metric Spaces with Lower Curvature Bounds

    by Areeyuth Sama-Ae

    In this paper, we examine geometric relationships between metric spaces with curvature bounded below and their corresponding model spaces of constant curvature. Let \(\gamma\) be a closed spherical curve in a metric space whose curvature is bounded below by \(K\), lying at a distance \(r < \tfrac{\pi}{2\sqrt{K}}\) from a point. Let \(\gamma^{\prime}\) denote the circle of radius \(r\) centered at the corresponding point in the model space of constant curvature \(K\). Under suitable geometric equivalence conditions—namely, the preservation of pairwise distances between corresponding points of \(\gamma\) and \(\gamma^{\prime}\), the isometry of convex hulls of corresponding geodesic triangles, and the equality of arc lengths or total curvature—we show that the geodesic surface enclosed by \(\gamma\) is isometric to the region bounded by \(\gamma^{\prime}\). This result offers a foundational geometric characterization of metric spaces with curvature bounded below through their model counterparts and provides a framework for further study of total curvature, convexity, and isometric embeddings in such spaces.

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    Ideal‐Driven β θ ‐I‐Open Sets and Their Role in Connectedness, Hyperconnectedness, and Extremal Disconnectedness

    by Naeem Nisar Sheikh, Chawalit Boonpok, Areeyuth Sama-Ae

    In this paper, we introduce a novel type of open set, called ‐open sets, constructed by means of an ideal on a topological space. These sets broaden the classical definition of openness. Employing these ideal‐based generalized open sets, we investigate essential topological properties—including connectedness, hyperconnectedness, and extremal disconnectedness—and derive results that unify, generalize, and sharpen earlier theories. The inclusion of ideals enhances the structural framework and yields new characterizations, demonstrating the versatility and broad relevance of these sets in both classical and ideal topological settings. Moreover, we analyze various classes of functions that preserve or reflect these properties between ideal topological spaces, offering a refined perspective on connectedness under different mappings.

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    Weakly $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous Multifunctions

    by Nongluk Viriyapong, Areeyuth Sama-Ae, Chawalit Boonpok

    This paper presents new classes of continuous multifunctions defined between an ideal topological space and a bitopological space, called upper weakly $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions and lower weakly $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions. Furthermore, several characterizations and some properties concerning upper weakly$\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions and lower weakly $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions are considered.

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    On Upper and Lower $\mu(\sigma_1,\sigma_2)$-continuous Multifunctions

    by Nipaporn Chutiman, Areeyuth Sama-Ae, Chawalit Boonpok

    This paper presents new concepts of continuous multifunctions defined from a generalized topological space into a bitopological space, called upper $\mu(\sigma_1,\sigma_2)$-continuous multifunctions and lower $\mu(\sigma_1,\sigma_2)$-continuous multifunctions. Furthermore, several characterizations and some properties concerning upper $\mu(\sigma_1,\sigma_2)$-continuous multifunctions and lower $\mu(\sigma_1,\sigma_2)$-continuous multifunctions are discussed.

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    On Upper and Lower Almost $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous Multifunctions

    by Chokchai Viriyapong, Areeyuth Sama-Ae, Chawalit Boonpok

    This paper introduces new classes of continuous multifunctions defined between an ideal topological space and a bitopological space, called upper almost $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions.Furthermore, several characterizations and some properties concerning upper almost $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous multifunctions are investigated.

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    On upper and lower weakly $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions

    by Montri Thongmoon, Areeyuth Sama-Ae, Chawalit Boonpok

    A new class of continuous multifunctions between an ideal topological space and a bitopological space,called upper (lower) weakly $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions, has been defined and studied. Furthermore, several characterizations and some properties concerning upper weakly$\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions and lower weakly $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions are discussed.

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    Almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuity for Multifunctions

    by Napassanan Srisarakham, Areeyuth Sama-Ae, Chawalit Boonpok

    This paper introduces new classes of continuous multifunctions defined between an ideal topological space and a bitopological space, called upper almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions. Moreover, several characterizations and some properties concerning upper almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions and lower almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions are established.

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