المصدر: locally connected and locally compact في منتدى : قسم الرياضيات السلام عليكم اخواني الافاضل ارجو مساعدتي في الاسئلة التالية 1) Show that every open subset of a locally connected topological space is itself locally connected 2) Show that a closed subset of a locally compact space is locally compact شكرا مقدما
Let X be locally compact and T2 If A is an open in X and a in A , Then a point a has a compact nhood K in X contained in A ,and K is then a compact nhood of a in A, so A is locally compact . And B is closed and b in B , then b has a compact nhood K in X and K∩B is a compact nhood of b in B ,so B is locally compact. وهذا من كتاب willard