Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, 0, {3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, p, {2}, {1,2,3}, %3D %3D {4,5,6}, {2,4,5,6}} * T1 is not a topology and T2 is a topology on T1 is a topology on X and T2 is not a topology on X O T1 and T2 are both topologies on X T1 and T2 are both not topologies on X

Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, 0, {3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, p, {2}, {1,2,3}, %3D %3D {4,5,6}, {2,4,5,6}} * T1 is not a topology and T2 is a topology on T1 is a topology on X and T2 is not a topology on X O T1 and T2 are both topologies on X T1 and T2 are both not topologies on X

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 68E: Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if...

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, 0, {3},
{1,2,3}, {2,3,4}, {2}} and T2 = {X, p, {2}, {1,2,3},
%3D
{4,5,6}, {2,4,5,6}} *
T1 is not a topology and T2 is a topology on
T1 is a topology on X and T2 is not a
topology on X
O T1 and T2 are both topologies on
X
T1 and T2 are both not topologies on X

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