In a topological space X, define x~y for points x,y∈X iff x and y are path connected. This is easily seen to be an equivalence relation; the set of equivalence classes X/~ (a partition of X into the sets of points with paths between them) is the set of the path connected components of X.

In other words, a path connected component of X is a maximal (with respect to inclusion) set of points with paths to some point.

Path connected components are not the same as connected components, although for "simple" topological spaces they coincide. They can be considered alternative generalizations of the notion of connected components in undirected graphs.

In the beginning of all you have,
when those five syllables of possibility
are as wide open to you as your hand,

what will separate you from everything
will be the place of your birth and the race of your people,
along with the year of your appearance

and the state of your genetic health,
the accident of your strength and bare agility,
the ability of the head you were issued with,

the capacity of your lungs
and the accurate connection of your bones and sinews.
One more thing before you walk through the door and out into your life;

stop at the mirror and confirm the matter of your sex,
almost 50% either way, but still of prime significance
as regards many aspects of your opportunity.

In the back end of what you had,
most will no longer talk of all you can be,
but instead assess you (if they look at all) for what you did and were,

partly in measure of all you began with,
but more often by the amount of your money
and the size of the self that others (like them)

have decided to see you as,
yet with any chance you will have bred
or come from a  family where ample breeding took place.

These people -at best and depending- will be the ones
who may truly see what you are and what you did,
who you were in consideration of the list you started out with.

It is also common that they may not
and in that way only you will know.
Good luck.

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