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Topic: Onto [0,1]
Replies: 40   Last Post: Apr 29, 2013 10:16 PM

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Tanu R.

Posts: 640
Registered: 12/13/04
Re: Onto [0,1]
Posted: Apr 25, 2013 7:00 PM
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Butch Malahide write:

> On Apr 25, 5:12 pm, quasi <qu...@null.set> wrote:
>> Prove or disprove:
>> If X is a topological space and f: X -> [0,1] is a
>> continuous surjection, then X has a subspace homeomorphic
>> to the Cantor set.

> No, X could have the discrete topology.

As opposed to a homogenous topology which continuosly
reaches all limits.

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