Continuity of topological spaces

Question

So in this exact problem $f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$. My question is, what if the space given does not mention anything like say space $Y$ is not given nor given as being Hausdorff, will the statement still hold?

score 3 · Accepted Answer · answered Mar 28 '18 at 01:19

3

Some condition is needed. If $Y$ is an indiscrete space, then every function $f:X\to Y$ is continuous, so one cannot hope to define such a function by continuity if one only knows its values on a proper subset.

answered Mar 28 '18 at 01:19

Angina Seng

158,341

So I am confused so if the statement doesnt specify as $Y$ being Hausdorff, the statement will not hold? – Aurora Borealis Mar 28 '18 at 01:20
The question is not about extending a partial function by continuity, but rather about two already defined functions. – JKEG Mar 28 '18 at 06:36

Continuity of topological spaces

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