We may also state two alternative definitions of , using either the sequential criterion or else using topology and open sets.<\/p>\n
Alternative definition number 1<\/b> Let ##f: X ->Y## be a function and let ##(x_n)## be a sequence in X converging to an element x in X, ie ##lim(x_n)=x in X## Then f is continuous at x iff and only if the sequence of function values converge to the image of x undr f, ie ##iff lim (f(x_n))=f(x) in Y## <\/p>\n
Alternative definition number 2<\/b> Let ##f: X ->Y## be a function. Then f is continuous if the inverse image maps open subsets of Y into open subsets in X. ie, ##AAA_(open)subeY =>f^(-1)(A) ## is open in X <\/p>\n","protected":false},"excerpt":{"rendered":"
We may also state two alternative definitions of , using either the sequential criterion or else using topology and open sets. Alternative definition number 1 Let ##f: X ->Y## be a function and let ##(x_n)## be a sequence in X Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-71877","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/71877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=71877"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/71877\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=71877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=71877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=71877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}