Continuous Lattices of Maps between T 0 Spaces 1 Grzegorz Bancerek University of Białystok

The articles [32], [15], [38], [33], [19], [39], [13], [40], [18], [12], [16], [1], [10], [30], [2], [35], [27], [28], [29], [37], [3], [14], [31], [24], [11], [42], [34], [4], [5], [6], [22], [41], [17], [8], [7], [25], [36], [23], [21], [26], and [9] provide the notation and terminology for this paper. Let I be a set and let J be a relational structure yielding many sorted set indexed by I. We introduce I -prodPOS J as a synonym of ∏J. Let I be a set and let J be a relational structure yielding nonempty many sorted set indexed by I. Observe that I -prodPOS J is constituted functions. Let I be a set and let J be a topological space yielding nonempty many sorted set indexed by I. We introduce I -prodTOP J as a synonym of ∏J. Let X , Y be non empty topological spaces. The functor [X → Y ] yields a non empty strict relational structure and is defined as follows: