We show that if X is a locally compact, paracompact and Hausdorff space, then X can be realised as the subspace of all maximal points of the inverse limit of an inverse system of partial orders with an appropriate topology (equivalently T0-Alexandroff spaces). Then, the space X is homeomorphic to a deformation retract of that limit. Moreover, we extend results obtained by Clader and Thibault an...

Let X be a box product of K many compact metric spaces. We give various models in which X/finite and X/countable are paracompact, as well as related re­ sults.

a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property t...

The concept of induced fuzzy topological space, introduced by Weiss [J. Math. Anal. Appl. 50(1975), 142-150], was defined with the notion of a lower semi-continuous function. The aim of this paper is to introduce and study the concepts of induced fuzzy supra-topological spaces and s-lower β-continuous functions. s-Lower β-continuous functions turn out to be the natural tool for studying the ind...