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<p>The aim of this paper is to introduce the concept of semi-Császár structures and investigate their relationship with the well-known notion of pre-nearness structures on frames. More explicitly, we define the category of semi-Császár frames and establish a connection with the category of covering pre-nearness frames. We provide conditions under which semi-Császár structures relate with pre-uniformities on frames. Finally, we present a frame counterpart to the relationship between symmetric syntopogenous structures and nearness spaces as established by Herrlich (Gen Topol Appl 4(3):191–212, 1974).</p>

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On Császár structures and pre-nearness on frames

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • David Holgate,
  • Bakulikira Iragi

摘要

The aim of this paper is to introduce the concept of semi-Császár structures and investigate their relationship with the well-known notion of pre-nearness structures on frames. More explicitly, we define the category of semi-Császár frames and establish a connection with the category of covering pre-nearness frames. We provide conditions under which semi-Császár structures relate with pre-uniformities on frames. Finally, we present a frame counterpart to the relationship between symmetric syntopogenous structures and nearness spaces as established by Herrlich (Gen Topol Appl 4(3):191–212, 1974).