The featured review of the AMS describes the author’s earlier work in the field of approach spaces as, ‘A landmark in the history of general topology’. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.

This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems. It focuses on two index theories: L-index theory (index theory for Lagrangian boundary conditions) and P-index theory (index theory for P-boundary conditions). In addition, the book introduces readers to recent advances in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations.

A rising proportion of the global population are moving to cities in search of a better standard of living. However, although urbanisation has its benefits, unchecked urbanisation can lead to a host of challenges, such as congestion and limited access to public services. As such, the concept of urban liveability has been garnering more attention from policymakers and academics who are interested in mitigating the negative effects of urbanisation.In this context, the Asia Competitiveness Institute (ACI) has released the 2018 Global Liveable and Smart Cities Index (GLSCI), the third in its series of liveability indices. The GLSCI attempts to measure the liveability of an average resident in a city. More importantly, this year's edition has added considerations to the concept of smart cities and the role that these technologies can play in augmenting the liveability of a city's residents. It also builds on ACI's past liveability indices by expanding the number of cities in the index to 78, notably with African cities for the first time. In addition, this book includes two case studies on liveability. The first one concerns the relationship between a city's liveability, smartness, connectivity, and agglomeration, while the other is a case study on the 99-year lease of public housing in Singapore.

India’s COVID-19 battle will be told and retold in the coming years, inspiring both praise for what the country has achieved, and critique for its shortfalls. As India’s story continues to unfold, two strands will mould the various assessments. First is India’s aggregate performance as a developing economy: It marshalled its meagre resources to respond to the exponential threat of the virus, and was determined, too, to be part of global solutions to this scourge, such as the manufacture and supply of life-saving vaccines. The second, and perhaps even more important story is on ground-zero: In its cities and villages, India’s success or failure would be a factor of the leadership and stewardship of Prime Minister Narendra Modi and his team in responding to the crisis, and the commitment of the chief ministers and state functionaries to beef up their health systems and save lives. Whichever way the India story is told, there are certain truths that cannot be hidden: We need to invest more in our health systems, and acknowledge the stellar role of our frontline workers and formal and informal health sector personnel, as well as India’s prowess in certain segments of the medical and health industry. In this context, it becomes interesting to see how in the country’s federal structure (where health is a State subject), the sub-national units—i.e., states and union territories (UTs)—have performed. The present work, Health Systems Resilience Index: A Sub-National Analysis of India’s COVID-19 Response, provides answers to that question. It builds on an earlier report published by the Observer Research Foundation in May 2020. That report, State of the States: Two Months of the Pandemic, evaluated India’s initial response to the pandemic shortly after the crisis was officially named by the World Health Organization (WHO). Two years since then, this report attempts a more ambitious goal: to devise a unique Resilience Index for the health systems of India’s states and UTs.