On page 113 Munkres (Topology: Second Edition) defines a J-tuple as follows:

I was somewhat perplexed when I tried to completely understand the function $\displaystyle \ x \ : \ J \to X $.

I tried to write down some specific and concrete examples but still could not see exactly how the function would work.

For example if $\displaystyle J = \{1, 2, 3 \} $ and X was just the collection of all the letters of the alphabet i.e.

$\displaystyle X = \{ a, b, c, ... \ ... \ z \} $ then ...

... obviously a map like 1 --> a, 2 --> d, 3 --> h does not work as the intention, I would imagine is to have a mapping which specifies a number of triples ... but how would this work?

[Just to clarify what I mean: I imagined, as an example a mapping by x such that

1 mapped to a

2 mapped to d

3 mapped to h

However, although this is a mapping from J to X under the function x it does not really define a set of triples.]

Can someone either correct my example or give a specific concrete example that works.

Would appreciate some help.

Peter