- #1

sa1988

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## Homework Statement

Which of the following topologies are Hausdorff (if any)?

{∅, {a,b} }

{∅, {a}, {a,b} }

{∅, {b}, {a,b} }

{∅, {a}, {b}, {a,b} }

## Homework Equations

Definitions:

A neighbourhood U of x is an open set U⊂X such that xϵU

A topological space is Hausdorff if for each pair x, y of distinct points in X there exist neighbourhoods U of x and V of y which are disjoint.

## The Attempt at a Solution

[/B]Another description I've seen for the Hausdorff property is that for some two subsets U and V in X, the intersection of U and V is the empty set.

Looking at the given topologies, it seems that only the last one is Hausdorff. One can take {a} and {b} and see that their intersection is ∅. .

Hoping I'm correct with this? I just wanted to put it by the physics forum crowd because topology is a new and potentially worrying subject I've taken on at university, with a lot of new definitions and terminology being thrown around at quite a fast pace!

Thanks