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<p>In this paper, we study the relative components defined by using relative versions of the topological property of connectedness. We use this concept to obtain a new type of spaces, which are located between 0-dimensional spaces and totally disconnected spaces, namely, the family of <i>totally disconnected</i><sub>5</sub> spaces. We also study some relations between the relative components in the hyperspace of closed and nonempty sets. We present a new proof of the well-known result that a quasi-component in a topological product is obtained as the product of quasi-components. Finally, we address a relationship between the relative components of a topological space <i>X</i> and the relative components of its hyperspace CL(<i>X</i>).</p>

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An Introduction to the Relative Components in Topological Spaces

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Florencio Corona–Vázquez,
  • Jesús Díaz–Reyes,
  • Russell–Aarón Quiñones–Estrella,
  • Javier Sánchez–Martínez

摘要

In this paper, we study the relative components defined by using relative versions of the topological property of connectedness. We use this concept to obtain a new type of spaces, which are located between 0-dimensional spaces and totally disconnected spaces, namely, the family of totally disconnected5 spaces. We also study some relations between the relative components in the hyperspace of closed and nonempty sets. We present a new proof of the well-known result that a quasi-component in a topological product is obtained as the product of quasi-components. Finally, we address a relationship between the relative components of a topological space X and the relative components of its hyperspace CL(X).