let x be at Plogy space and Suppoes that anbhd bea basic has been fixed at Cachxe X Prove that Fr={xex/each basicnbhdofx € meets both A and A. ASX is open ifs A con tians abasic nbhd of each its point, ③If A EN (x) then there exist B EN(X) and BCA ST AEN(Y) for each yeB. Can you create a toplogy from nbhd basic with prove.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 62E
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let x be at Plogy space and
Suppoes that anbhd bea
basic has been fixed at
Cachxe X
Prove that
Fr={xex/each basicnbhdofx
€
meets both A and A.
ASX is open ifs A con tians
abasic nbhd of each its point,
③If A EN (x) then there exist B
EN(X) and BCA ST AEN(Y)
for each yeB.
Can you create a toplogy from
nbhd basic with prove.
Transcribed Image Text:let x be at Plogy space and Suppoes that anbhd bea basic has been fixed at Cachxe X Prove that Fr={xex/each basicnbhdofx € meets both A and A. ASX is open ifs A con tians abasic nbhd of each its point, ③If A EN (x) then there exist B EN(X) and BCA ST AEN(Y) for each yeB. Can you create a toplogy from nbhd basic with prove.
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