THE HALF DISC TOPOLOGY IS PARTIALLY METRIZABLE

Samer Assaf; Tom Cuchta

THE HALF DISC TOPOLOGY IS PARTIALLY METRIZABLE

Samer Assaf
, Tom Cuchta

Mathematic and Natural Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we answer the long standing conjecture: “Is a Hausdorff partial metric space metrizable?”, albeit in a negative way. To accomplish this, we show how to partially metrize the Half Disc Topological Space, a non-metrizable Completely Hausdorff space. We end by suggesting a new conjecture to replace the one we disproved.

Original language	English
Pages (from-to)	139-144
Number of pages	6
Journal	Topology Proceedings
Volume	61
State	Published - 2023

Keywords

completely hausdorff
half disc topology
partial metric
separation axiom

Cite this

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title = "THE HALF DISC TOPOLOGY IS PARTIALLY METRIZABLE",

abstract = "In this paper we answer the long standing conjecture: “Is a Hausdorff partial metric space metrizable?”, albeit in a negative way. To accomplish this, we show how to partially metrize the Half Disc Topological Space, a non-metrizable Completely Hausdorff space. We end by suggesting a new conjecture to replace the one we disproved.",

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AB - In this paper we answer the long standing conjecture: “Is a Hausdorff partial metric space metrizable?”, albeit in a negative way. To accomplish this, we show how to partially metrize the Half Disc Topological Space, a non-metrizable Completely Hausdorff space. We end by suggesting a new conjecture to replace the one we disproved.

KW - completely hausdorff

KW - half disc topology

KW - partial metric

KW - separation axiom

UR - https://www.scopus.com/pages/publications/85156184550

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SN - 0146-4124

VL - 61

SP - 139

EP - 144

JO - Topology Proceedings

JF - Topology Proceedings

ER -

THE HALF DISC TOPOLOGY IS PARTIALLY METRIZABLE

Abstract

Keywords

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