Let B = {[a, b) CR| a < b}. (a) Show that B is a basis for a topology on R called the lower limit topology, denoted RỊ. (b) Determine which of the following are open in R: A = D = (7,8). [4, 5), B = {3}, C = [1, 2),

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A: Answer given below.

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Q: 5.61. For each linear map F find a basis and the dimension of the kernel and the image of F: (a)F:R…

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A: Let us consider the two topologies, T" data-mce-style="display: inline-table; font-style: normal;…

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A: Note: According to bartleby we have to solve only first question please upload the question…

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