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Let X be a non- empty set and Let de : X xX→ [0,0) be a function. If the following condition hold for any X, Y, Z EX : is If dq (Xgy) E dq (I9x)=0 , then x=y ; ii» de (xox) s dq (x,2) + dq (2,y). Then pair (X,dz) is called a dis located qua si me tric Space. Let X= R* U j0} and dg (x,y)=x+max}x,y} for any X,y E x. Then prove that (X, dq). is dislocated quasi metnic Space - a

Let X be a non- empty set and Let de : X xX→ [0,0) be a function. If the following condition hold for any X, Y, Z EX : is If dq (Xgy) E dq (I9x)=0 , then x=y ; ii» de (xox) s dq (x,2) + dq (2,y). Then pair (X,dz) is called a dis located qua si me tric Space. Let X= R* U j0} and dg (x,y)=x+max}x,y} for any X,y E x. Then prove that (X, dq). is dislocated quasi metnic Space - a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let X be a non- empty set and : X xX [0,0) be a function. If the following condition hold for any X, Yo Z EX : ir If dg (x,y) = dg (Y2x)=0, then xay ; Lii da (x,y) s da(x,z) + dq (z,y). Then paiy (X,dy) is called a dis located qua si me tric Space. Let X= R* u j0} and da (x,y)=x+max, that (Xg dq) for any x,y € X. Then dislocated prove is quasi metnic Space. a
Transcribed Image Text:Let X be a non- empty set and : X xX [0,0) be a function. If the following condition hold for any X, Yo Z EX : ir If dg (x,y) = dg (Y2x)=0, then xay ; Lii da (x,y) s da(x,z) + dq (z,y). Then paiy (X,dy) is called a dis located qua si me tric Space. Let X= R* u j0} and da (x,y)=x+max, that (Xg dq) for any x,y € X. Then dislocated prove is quasi metnic Space. a
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