converges homeomorphically to the continuum

The statement that the sequence $M_1, M_2, \cdots$ converges homeomorphically to the continuum M means there exists a sequence $h_1, h_2, \cdots$ of homeomorphisms such that, for each positive integer i, h_i is a homeomorphism from M_i onto M and for each positive number $\varepsilon$ there exists a positive integer N such that if j > N then, for all x, dist $(h_j(x),x) < \varepsilon$.