Lipschitz quotient mappings and uniform quotient mappings between Banach spaces are introduced and investigated. In particular, it is shown that if a Banach space is a uniform quotient of L p , 1 < p < ∞, then it is isomorphic to a linear quotient of L p. For the purpose of studying quotient mappings and also for their own interest, new concepts related to approximating general Lipschitz functi...

In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling definitions, and is further justified by a number of results. Quotient stacks are very closely related to quotient spaces; for example, when the orbifold group ac...

In 1966, Michael [11] introduced the concept of compact-covering maps. Since many important kinds of maps are compact-covering, such as closed maps on paracompact spaces, much work has been done to seek the characterizations of metric spaces under various compact-covering maps, for example, compact-covering (open) s-maps, pseudosequence-covering (quotient) s-maps, sequence-covering (quotient) s...

To determine what spaces are the images of “nice” spaces under “nice” mappings is one of the central questions of general topology in 1 . In the past, many noteworthy results on images of metric spaces have been obtained. For a survey in this field, see 2 , for example. A characterization for a quotient compact image of a locally separable metric space is obtained in 3 . Also, such a quotient i...

We study an extensive connection between quotient forcings of Borel subsets of Polish spaces modulo a σ-ideal and quotient forcings of subsets of countable sets modulo an ideal.

We give a construction of coequalisers in formal topology, a predicative version of locale theory. This allows for construction of quotient spaces and identification spaces in constructive topology.

We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.