(1) In this problem, we view the set X = {-1,0, 1) as a topological space with the quotient topology from the function f

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1 In This Problem We View The Set X 1 0 1 As A Topological Space With The Quotient Topology From The Function F 1 (14.34 KiB) Viewed 35 times

(1) In this problem, we view the set X = {-1,0, 1) as a topological space with the quotient topology from the function f: RX defined by the formula T>0 f(x) = {0 (a) List the open subsets of X. (b) Is X compact? (c) Is X connected? (d) Is X path connected? (e) Is X Hausdorff? (f) Is f an open map? (g) Is f a closed map? (-1 #40 (2) Let f: XY be a continuous map between path connected, locally path connected, and compla the al