A sequence of inclusions whose colimit is not a homotopy colimit

Benjamin Branman, Igor Kriz, Aleš Pultr
2015 New York Journal of Mathematics New York J. Math   unpublished
It is known that the homotopy colimit of a sequence of inclusions of T1 spaces is weakly equivalent with the actual colimit. We show that the assumption of T1 is essential by providing a counterexample for non-T1 spaces.