An Arzelà-Ascoli theorem for asymmetric metric spaces (sometimes called quasi-metric spaces) is proved. One genuinely asymmetric condition is introduced, and it is shown that several classic statements fail in the asymmetric context if this assumption is dropped.

We present the complete classification of the subgroup of the classical knot concordance group generated by knots with eight or fewer crossings. Proofs are presented in summary. We also describe extensions of this work to the case of nine crossing knots.

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Exposure to asbestos fibres causes asbestosis, mesothelioma and several other cancers, which together are commonly referred to as asbestos-related diseases (ARDs). The use of asbestos increased rapidly in Australia and overseas throughout the 1900s, but knowledge about the health effects of exposure and subsequent controls came about more gradually. In Australia today, an estimated 4000 people still die annually from ARDs. While most of these deaths are due to past occupational exposures, there is ongoing concern about the many potential sources of asbestos exposure remaining in homes and the broader built environment as a legacy of past use. Current evidence indicates that Australians will continue to be exposed to legacy asbestos occupationally and non-occupationally, and continue to develop ARDs, without targeted action to prevent it. Evidence of ongoing exposure highlights the importance of better understanding how and why such exposures might still occur, and how they can be effectively prevented or controlled, with the aim of preventing the disease in the future. A better characterisation of this risk is also necessary to enable effective risk management and appropriate risk communication that is relevant to the current Australian context. This article explores the past, present and future of ARDs in Australia, considers the risk of a new wave of ARDs from legacy asbestos, and identifies where further study is required so that sustainable policies and practices can be developed to prevent a future wave of diseases.

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