Topologies on spaces of subsets

Topologies on Spaces of Subsets

On Generalized Injective Spaces in Generalized Topologies

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

Topologies on IR” induced by smooth subsets

Ancel, F.D., Topologies on Iw” induced by smooth subsets, Topology and its Applications 43 (1992) 189-201. If Y is a collection of subsets of iw”, let Y!? denote the largest topology on Iw” which restricts to the standard topology on each element of Y, and let ?t$ denote the homeomorphism group of Iw” wtth the topology &. Let Y_, denote the standard topology on Iw” and let %?_d denote the homeo...

Natural topologies on function spaces

ing the above, for a (not necessarily countable) family . . . φ2 // B1 φ1 // Bo of Banach spaces with continuous linear transition maps as indicated, not recessarily requiring the continuous linear maps to be injective (or surjective), a (projective) limit limiBi is a topological vector space with continuous linear maps limiBi → Bj such that, for every compatible family of continuous linear map...

On Topologies for Function Spaces

Given topological spaces Xt ÜT, and F and a function h from XXT to F which is continuous in x for each fixed ty there is associated with h a function h* from I t o F = F x , the space whose elements are the continuous functions from X to F. The function h* is defined as follows: h*(t)=ht, where ht(x)~h(x} t) for every x in X. The correspondence between h and h* is obviously one-to-one. Although...