Hi Mario,

| If you know of an existing formalization of elementary topology in HOL4
| please let me know, so that I can avoid duplicating work.

Not in HOL4, but in HOL Light there is quite a bit of topology, which
might at least serve as inspiration, if not something to port. See the
various files here:

  https://github.com/jrh13/hol-light/tree/master/Multivariate

Most of it is rooted in the special case of R^n, but there is one file
with purely general topology and metric spaces:

  https://github.com/jrh13/hol-light/tree/master/Multivariate/metric.ml

John.

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