626 research outputs found
A characterization of submanifolds by a homogeneity condition
A very short proof of the following smooth homogeneity theorem of D. Repovs,
E. V. Scepin and the author is presented.
Let N be a locally compact subset of a smooth manifold M. Assume that for
each two points x,y in N there exist their neighborhoods Ux and Uy in M and a
diffeomorphism h : Ux \to Uy such that h(x)=y and h (Ux \cap N) = Uy \cap N.
Then N is a smooth submanifold of M.Comment: 4 pages, meaning-distorting typos correcte
Detecting codimension one manifold factors with topographical techniques
We prove recognition theorems for codimension one manifold factors of
dimension . In particular, we formalize topographical methods and
introduce three ribbons properties: the crinkled ribbons property, the twisted
crinkled ribbons property, and the fuzzy ribbons property. We show that is a manifold in the cases when is a resolvable
generalized manifold of finite dimension with either: (1) the
crinkled ribbons property; (2) the twisted crinkled ribbons property and the
disjoint point disk property; or (3) the fuzzy ribbons property
Topics in uniform continuity
This paper collects results and open problems concerning several classes of
functions that generalize uniform continuity in various ways, including those
metric spaces (generalizing Atsuji spaces) where all continuous functions have
the property of being close to uniformly continuous
On countably compact 0-simple topological inverse semigroups
We describe the structure of 0-simple countably compact topological inverse
semigroups and the structure of congruence-free countably compact topological
inverse semigroups
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