التحليل locally connected and locally compact

[hanin]

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

 

[terooz]

Let X be locally compact and T2​

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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 .​

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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.​

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وهذا من كتاب willard ​

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[medodido]

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