Characterization of arcs by products and diagonals

Authors

  • Hidefumi Katsuura San Jose State University

Keywords:

continuum, arc, Hausdorff arc, product, diagonal, cut point, non-cut point, linearly ordered topological space

Abstract

We prove that a continuum $X$ is a Hausdorff arc if, and only if, $X^2-D$ is not connected, where $D$ is the diagonal of $X^2$.

References

J.G. Hocking and G. S. Young, Topology, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts; London; 1961.

S. Nadler, Continuum Theory: An Introduction, Marcel Dekker, Inc., New York, N.Y., 1992.

S. Willard, General Topology, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts; Menlo Park, California; London, Amsterdam; Don Mills; Ontario; Sydney, 1970.

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Published

2022-11-26

How to Cite

Katsuura, H. (2022). Characterization of arcs by products and diagonals. Topology Proceedings, 63, 1–4. Retrieved from https://topology.journals.yorku.ca/index.php/tp/article/view/149

Issue

Vol. 63 (2024)

Section

Uncategorized