Does this form a topology?


by blahblah8724
Tags: intersection, topology
blahblah8724
blahblah8724 is offline
#1
Feb27-12, 10:48 AM
P: 32
I am told that the interval (a, ∞) where a [itex]\in[/itex] (0, ∞) together the empty set and [0, ∞) form a topology on [0, ∞).

But I thought in a topology that the intersection if any two sets had to also be in the topology, but the intersection of say (a, ∞) with (b, ∞) where a<b is surely (a,b) which isn't in the topology?

Help! Thanks!
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
arkajad
arkajad is offline
#2
Feb27-12, 11:13 AM
P: 1,412
Given any nonepty set X, the collection (empty set, X) is a topology. It is called "trivial topology". Please, check that it indeed satisfies all the axioms of a topological space.
AdrianZ
AdrianZ is offline
#3
Feb27-12, 11:18 AM
P: 320
Quote Quote by blahblah8724 View Post
I am told that the interval (a, ∞) where a [itex]\in[/itex] (0, ∞) together the empty set and [0, ∞) form a topology on [0, ∞).

But I thought in a topology that the intersection if any two sets had to also be in the topology, but the intersection of say (a, ∞) with (b, ∞) where a<b is surely (a,b) which isn't in the topology?

Help! Thanks!
the intersection of (a,∞) and (b,∞) where a<b is (b,∞), not (a,b).


Register to reply

Related Discussions
[topology] compact, locally connected, quotient topology Calculus & Beyond Homework 2
The usual topology is the smallest topology containing the upper and lower topology Topology and Analysis 2
The usual topology is the smallest topology containing the upper and lower topology Calculus & Beyond Homework 0
Topology question - Compact subset on the relative topology Calculus & Beyond Homework 1
What's the difference between differential topology and algebraic topology? Differential Geometry 5