Infinite-dimensional spaces are ubiquitous inmany branches of mathematics, and their topologies are almost always interesting. Samples of spaces that one is sure to encounter are Cc(R), C (R), L(R), and their continuous linear duals. There are two good reasons for making oneself at least somewhat familiar with the subject. On the one hand, without some preparation, it is easy to make false stat...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...