necessarily discreteA subspace of an indiscrete space isdiscreteEvery subspace of a discrete space isdiscreteLet X = {a, b, c, d} and TX = {Ø, X, {b}, {b,c},{a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4}and TY = {Ø, Y, {3}, {1,2,3}} be a topology onY. Let f be a mapping from X into Y definedby f(a)=4, f(b) = 3, f(c) = 2 and f(d) = 4. Let gbe mapping from X into Y defined by g(a) =1, g(b)=g(c)=D3 and g(d) = 4. Then *f and g are not continuousf and g are both continuousf is not continuous and g is continuousf is continuous and g is not continuousLet X = {a, b, c, d,e} and let T = {X, Ø, {a},{a,d}, {a,e}}, then *O (X,T) is not connected but it is Hausdorff

Let X = {a, b, c, d} and TX = {Ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4} and TY = {Ø, Y, {3}, {1,2,3}} be a topology on Y. Let f be a mapping from X into Y defined by f(a)=4, f(b) = 3, f(c) = 2 and f(d) = 4. Let g %3D %3D %3D be mapping from X into Y defined by g(a) = 1, g(b)=g(c)=3 and g(d) = 4. Then * O f and g are not continuous O f and g are both continuous O fis not continuous and g is continuous f is continuous and g is not continuous

Let X = {a, b, c, d} and TX = {Ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4} and TY = {Ø, Y, {3}, {1,2,3}} be a topology on Y. Let f be a mapping from X into Y defined by f(a)=4, f(b) = 3, f(c) = 2 and f(d) = 4. Let g %3D %3D %3D be mapping from X into Y defined by g(a) = 1, g(b)=g(c)=3 and g(d) = 4. Then * O f and g are not continuous O f and g are both continuous O fis not continuous and g is continuous f is continuous and g is not continuous

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 30E

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