Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  define and study hierarchies of topological spaces induced by the classical Borel and Luzin hierarchies of sets. Our hierarchies are divided into two classes: hierarchies of countably based spaces induced by their embeddings into the domain P\omega, and hierarchies of spaces (not necessarily countably based) induced by their admissible representations.  concentrate on the non-collapse property of the hierarchies and on the relationships beten hierarchies in the two classes.
['Matthias Schroeder', 'Victor L. Selivanov']
I am writing a research paper on a idea Some Hierarchies of QCB_0-Spaces
[{"from": "human", "value": "I am writing a research paper on a idea Some Hierarchies of QCB_0-Spaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  define and study hierarchies of topological spaces induced by the classical Borel and Luzin hierarchies of sets. Our hierarchies are divided into two classes: hierarchies of countably based spaces induced by their embeddings into the domain P\\omega, and hierarchies of spaces (not necessarily countably based) induced by their admissible representations.  concentrate on the non-collapse property of the hierarchies and on the relationships beten hierarchies in the two classes."}]