Orbifold transversality

We prove a best possible transversality theorem for maps from manifolds to orbifolds, and, more generally arbitrary differentiable Deligne–Mumford classifying champs, 0.1, of groupoids $$R\rightrightarrows U$$ R ⇉ U in separated, 0.2, manifolds. En passant, the essentially finite dimensional linear algebra nature of jet transversality is isolated.

Coincidence Continuation Theory for Multivalued Maps with Selections in a Given Class

This paper considers the topological transversality theorem for general multivalued maps which have selections in a given class of maps.

A Topological Coincidence Theory for Multifunctions via Homotopy

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.

A Note on the Topological Transversality Theorem for Weakly Upper Semicontinuous, Weakly Compact Maps on Locally Convex Topological Vector Spaces

A simple theorem is presented that automatically generates the topological transversality theorem and Leray–Schauder alternatives for weakly upper semicontinuous, weakly compact maps. An application is given to illustrate our results.

The Topological Transversality Theorem for Multivalued Maps with Continuous Selections

This paper considers a topological transversality theorem for multivalued maps with continuous, compact selections. Basically, this says, if we have two maps F and G with continuous compact selections and F ≅ G , then one map being essential guarantees the essentiality of the other map.

Some General Theorems for Compact Acyclic Multifunctions

We present general Leray-Schauder type theorems for compact acyclic Multifunctions, using the topological transversality theorem by the author.

Transversality of smooth definable maps in O-minimal structures

We present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smooth topology. Finally, we prove a definable version of a theorem of Trotman which says that the Whitney (a)-regularity of a stratification is necessary and sufficient for the stability of transversality.