Need answer ASAP. Thank youuu! Let T and Te denote the standard topology and the lower-limit topology on R,respectively. Consider the basis B = J× T₂ for a topology in R2 = R XR and let Jp := (B).(a) Prove that the half-plane {(x, y) = R² | y ≥ 0} is open with respect to Tp.(b) Prove that the half-plane {(x, y) = R² | x ≥ 0} is not open with respect to Tp.

Answered: Image /qna-images/answer/09d0b209-257b-4436-bec8-99c358e90ba1.jpg

Let J and Je denote the standard topology and the lower-limit topology on R, respectively. Consider the basis B = T × T₂ for a topology in R² = R XR and let Jp := (B). (a) Prove that the half-plane {(x, y) = R² | y ≥ 0} is open with respect to Tp. (b) Prove that the half-plane {(x, y) = R² | x ≥ 0} is not open with respect to Tp.

Let J and Je denote the standard topology and the lower-limit topology on R, respectively. Consider the basis B = T × T₂ for a topology in R² = R XR and let Jp := (B). (a) Prove that the half-plane {(x, y) = R² | y ≥ 0} is open with respect to Tp. (b) Prove that the half-plane {(x, y) = R² | x ≥ 0} is not open with respect to Tp.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 49E

See similar textbooks