\n Determine which of the following collection of subsets of R are bases: solve each one individually.\n <\/p>\n
\n a) C1 = {(n,n+2)\u00a0\u2286 R | n\u2208Z}\n <\/p>\n
\n b) C2 = {[a,b]\u00a0\u2286 R | a<b}\n <\/p>\n
\n c) C3 = {[a,b]\u00a0\u2286 R | a<=b}\n <\/p>\n
\n d) C4 = {(-x,x)\u00a0\u2286 R | x\u2208R}\n <\/p>\n
\n e) C5 = {(a,b)\u00a0\u222a {b+1}\u00a0\u2286 R | a<b}\n <\/p>\n
\n Let B be the collection of subsets of Z used in defining the digital line topology. Show that B is a basis for a topology Z.\n <\/p>\n
Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"
Determine which of the following collection of subsets of R are bases: solve each one individually. a) C1 = {(n,n+2)\u00a0\u2286 R | n\u2208Z} b) C2 = {[a,b]\u00a0\u2286 R | a<b} c) C3 = {[a,b]\u00a0\u2286 R | a<=b} d) C4 = {(-x,x)\u00a0\u2286 R | x\u2208R} e) C5 = {(a,b)\u00a0\u222a {b+1}\u00a0\u2286 R | a<b} Let B be […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/228309"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=228309"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/228309\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=228309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=228309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=228309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}