{"product_id":"topological-spaces-as-generalized-distance-darrell-hajek-9798460199235","title":"Topological Spaces as Generalized Distance Spaces","description":"This book is a study of interrelationships of metric spaces, uniform spaces and (general) topological spaces.\u003cbr\u003eIt introduces a \"\u003ci\u003edistance\u003c\/i\u003e\" definition generalizing the one used for metric spaces. This generalized \u003ci\u003edistance\u003c\/i\u003e supports natural generalizations of continuity and uniform continuity in the more familiar context of metric spaces.\u003cbr\u003eMost constructs of general topology can be derived from these generalized distances type considerations, and they support the concept of \"uniform continuity\" in contexts even more general than traditional \u003ci\u003euniform\u003c\/i\u003e spaces.\u003cbr\u003eThese generalized definitions permit the definition of DST, the category of distance spaces and (generalized) continuous functions, and this category turns out to be isomorphic to TOP, the category of topological spaces and (topologically) continuous functions. Hence all subcategories of TOP also determine associated subcategories of DST just as subcategories of DST will determine subcategories of TOP.\u003cbr\u003eAmong the DST subcategories are: \u003cbr\u003e\u003ci\u003eD0 distance spaces\u003c\/i\u003e, which are associated with T0 topological spaces.\u003cbr\u003e\u003ci\u003eDR0 distance spaces\u003c\/i\u003e, which are associated with R0 topological spaces.\u003cbr\u003e\u003ci\u003eD1 distance spaces\u003c\/i\u003e, which are associated with T1 topological spaces.\u003cbr\u003e\u003ci\u003eDivisible distance spaces\u003c\/i\u003e, which are associated with regular topological spaces, and also with locally uniform spaces.\u003cbr\u003e\u003ci\u003eUniformly divisible distance spaces\u003c\/i\u003e, which are associated with completely regular topological spaces, and also with uniform spaces.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Darrell Hajek\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9798460199235\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Independently Published\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/19\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 116\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.36lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.24d","brand":"Darrell Hajek","offers":[{"title":"Paperback","offer_id":47579993800959,"sku":"9798460199235","price":22.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_ff66a9b4-4717-4b05-a659-99d82a37de20.jpg?v=1763878054","url":"https:\/\/www.whiterainbookhouse.com\/products\/topological-spaces-as-generalized-distance-darrell-hajek-9798460199235","provider":"WR Book House","version":"1.0","type":"link"}