{"product_id":"frames-and-locales-topology-without-points-paperback","title":"Frames and Locales: Topology Without Points - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eJorge Picado\u003c\/b\u003e (Author), \u003cb\u003eAles Pultr\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eUntil the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a \"realistic\" place (spot, grain) of non-trivial extent.\u003c\/p\u003e\u003cp\u003eImitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory.\u003c\/p\u003e\u003cp\u003eNo monograph of this nature has appeared since Johnstone's celebrated \u003ci\u003eStone Spaces\u003c\/i\u003e in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eUntil the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the 1920s offered an expression of the geometric intuition of a \"realistic\" place (spot, grain) of non-trivial extent.\u003c\/p\u003e\u003cp\u003eImitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the 1950s. It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory.\u003c\/p\u003e\u003cp\u003eNo monograph of this nature has appeared since Johnstone's celebrated \u003ci\u003eStone Spaces\u003c\/i\u003e in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 398\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1 x 9.1 x 6.1 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 22, 2011\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704858734899,"sku":"9783034801539","price":112.28,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/TEdNd0NGUXVaMmV1UDNWQ082bXJmQT09.webp?v=1763366288","url":"https:\/\/www.vysn.com\/en-ca\/products\/frames-and-locales-topology-without-points-paperback","provider":"VYSN","version":"1.0","type":"link"}