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the given below class of the open-closed (clopen) intervals in the real line R is the base of the upper limit topology. B = { (a, b] : a, b in R, a < b } You can see, R (set of real numbers) is the union of the members of B because every real number belongs to some open closed interval. Similarly, the given below class of the closed-open (clopen) intervals in the real line R is the base of the lower limit topology. B = { [a, b) : a, b in R, a < b }. for further detail, find given below book with complete details. General Topology by Schaum's Outline Page # 88 Chapter # 6 Chapter Name: Bases and Sub-Bases
G bilkul ap thek keh rhy lekn hm ny un open sets k intersections ko consider krna ha jo Base k open sets ko generate krn aur ap delh skty ho k base ka hr open set generate ho rha ha to hm keh skty hn k S_1 is a sub-base for given topology.
