We show that a continuous surjection of [0,1] onto a Euclidean Peano continuum X can be computed uniformly from a name of X as a compact set and a local connectivity operator for X. We show by meansâ€¦ (More)

The construction of a homing tour is known to be NP-complete. On the other hand, the Euler formula puts sufficient restrictions on plane graphs that one should be able to assert the existence of suchâ€¦ (More)

We investigate, and prove equivalent, effective versions of local connectivity and uniformly local arcwise connectivity for connected and computably compact subspaces of Euclidean space. We alsoâ€¦ (More)