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Semilinear (Topological) Spaces and Applications: June, 1971
Excerpt from Semilinear (Topological) Spaces and Applications: June, 1971
In this paper we define semivector spaces and develop some of their algebraic aspects including some structure theory; then top 0pogize these spaces to obtain semilinear topological spaces for which we identify a hierarchy of local convexity axioms; establish a number of fixed point and minmax theorems for spaces with various local convexity properties; illustrate how the spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces; and, finally, indicate briefly how all the above are applied in socio-economic analysis and optimization.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
In this paper we define semivector spaces and develop some of their algebraic aspects including some structure theory; then top 0pogize these spaces to obtain semilinear topological spaces for which we identify a hierarchy of local convexity axioms; establish a number of fixed point and minmax theorems for spaces with various local convexity properties; illustrate how the spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces; and, finally, indicate briefly how all the above are applied in socio-economic analysis and optimization.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
88 pages, Hardcover
First published August 5, 2015
About the author
Prem Prakash
57 books3 followersPrem Prakash has been practicing yoga and related arts and sciences since 1979. In 1990, his yoga guru, Baba Hari Dass, gave him permission to teach others. Prem Prakash and his wife, Ambika, (Lesley Gibbs) have studied formally with teachers from several different lineages, and together they serve as Co-Directors of the Green Mountain School of Yoga in Middlebury, Vt.
Prem Prakash is the author of The Yoga of Spiritual Devotion : A Modern Translation of the Narada Bhakti Sutras, Three Paths of Devotion : Goddess, God, and Guru, Yoga American Style, and Universal Yoga : The Bhagavad Gita for Modern Times. Prem Prakash has taught yoga throughout North America, and his writings have appeared in Yoga Journal, Yoga International, Light of Consciousness, Himalayan Path, and Yoga Aktuel (German).
In 2007, Prem Prakash was honored by the Institute of the Himalayan Tradition with their Annual Service Award. In 2008, the Institute recognized him as a Yogiraj, “an accomplished yogi who lives in the world.”
Prem Prakash is the author of The Yoga of Spiritual Devotion : A Modern Translation of the Narada Bhakti Sutras, Three Paths of Devotion : Goddess, God, and Guru, Yoga American Style, and Universal Yoga : The Bhagavad Gita for Modern Times. Prem Prakash has taught yoga throughout North America, and his writings have appeared in Yoga Journal, Yoga International, Light of Consciousness, Himalayan Path, and Yoga Aktuel (German).
In 2007, Prem Prakash was honored by the Institute of the Himalayan Tradition with their Annual Service Award. In 2008, the Institute recognized him as a Yogiraj, “an accomplished yogi who lives in the world.”
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