New PDF release: A Banach-Stone Theorem for Uniformly Continuous Functions

By Garrido M. I., Jaramillo J. A.

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Extra info for A Banach-Stone Theorem for Uniformly Continuous Functions

Sample text

SACHS Almost everyone who ever lived was wretchedly poor. Famine, death from childbirth, infectious disease and countless other hazards were the norm for most of history. Humanity’s sad plight started to change with the Industrial Revolution, beginning around 1750. New scientific insights and technological innovations enabled a growing proportion of the global population to break free of extreme poverty. 5 billion people can reliably meet their basic living needs and thus can be said to have escaped from the precarious conditions that once governed everyday life.

The shift will come fi rst and most acutely in the more developed countries, whereas the least developed countries will experience a slow increase in elderly dependency after 2020. By 2050 the elderly dependency ratio of the least developed countries will approach that of the more developed countries in 1950. Extrapolating directly from age to economic and social burdens is unreliable, however. The economic burden imposed by elderly people will depend on their health, on the economic institutions available to offer them work, and on the social institutions on hand to support their care.

C. showed that the Babylonians feared the world was already too full of people. In 1798 Thomas Malthus renewed these concerns, as did Donella Meadows in her 1972 book The Limits to Growth. While some people have fretted about too many people, optimists have offered reassurance that deities or technology will provide for humankind’s well-being. Early efforts to calculate Earth’s human carrying capacity assumed that a necessary condition for a sustainable human society could be measured in units of land.

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A Banach-Stone Theorem for Uniformly Continuous Functions by Garrido M. I., Jaramillo J. A.


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