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6. (i) Let f: (X, J) → (Y, U), where (X, T) and (Y, U) are two topolog- ical spaces. Show that if (X, J) is a discrete space, then f is continuous. (ii) Let X = {a,b,c}. construct two topologies T₁ and T₂ on X. Then define a function f: (X, J₁)→ (X, J₂) so that f is continuous.

6. (i) Let f: (X, J) → (Y, U), where (X, T) and (Y, U) are two topolog- ical spaces. Show that if (X, J) is a discrete space, then f is continuous. (ii) Let X = {a,b,c}. construct two topologies T₁ and T₂ on X. Then define a function f: (X, J₁)→ (X, J₂) so that f is continuous.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 7E
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6. (i) Let f (X, J) → (Y, U), where (X, J) and (Y, U) are two topolog- ical spaces. Show that if (X, T) is a discrete space, then f is continuous. (ii) Let X = {a,b,c}. construct two topologies T₁ and J₂ on X. Then define a function f (X, J₁)→ (X, J₂) so that f is continuous. :
Transcribed Image Text:6. (i) Let f (X, J) → (Y, U), where (X, J) and (Y, U) are two topolog- ical spaces. Show that if (X, T) is a discrete space, then f is continuous. (ii) Let X = {a,b,c}. construct two topologies T₁ and J₂ on X. Then define a function f (X, J₁)→ (X, J₂) so that f is continuous. :
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