Space S000124

Roy's lattice subspace

Let XX denote Roy's lattice space. Roy's lattice subspace is X{ω}X \setminus \{\omega\} with the subspace topology.

Defined as counterexample #127 ("Roy's Lattice Subspace") in DOI 10.1007/978-1-4612-6290-9.

Roy's lattice subspace is a counterexample to the converse of 5 theorems
Id If Then
T45 Extremally disconnectedT2T_2 Totally separated
T208 IndiscreteHas multiple points ¬Has an isolated point
T263 Hereditarily LindelöfScattered Countable
T450 Indiscrete Second countable
T508 RegularLindelöfScatteredHas points GδG_\delta Countable