Semi-local simple connectedness of non-collapsing Ricci limit spaces
نویسندگان
چکیده
Let $X$ be a non-collapsing Ricci limit space and let $x\in X$. We show that for any $\epsilon>0$, there is $r>0$ such every loop in $B_t(x)$ contractible $B_{(1+\epsilon)t}(x)$, where $t\in(0,r]$. In particular, semi-locally simply connected.
منابع مشابه
On Low Dimensional Ricci Limit Spaces
We call a Gromov-Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. In this paper, we prove that any Ricci limit space has integral Hausdorff dimension provided that its Hausdorff dimension is not greater than two. We also classify one-dimensional Ricci limit spaces.
متن کاملUniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces
We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...
متن کاملGeneralized semi-pre connectedness in intuitionistic fuzzy topological spaces
In this paper we have introduced the intuitionistic fuzzy generalized semi-pre connected space, intuitionistic fuzzy generalized semipre super connected space and intuitionistic fuzzy generalized semi-pre extremally disconnected space. We investigated some of their properties. Also we characterized the intuitionistic fuzzy generalized semi-pre super connected space. 2010 AMS Classification: 54A...
متن کاملSimple connectedness of hyperplane complements in dual polar spaces
Suppose ∆ is a dual polar space of rank n and H is a hyperplane of ∆. Cardinali, De Bruyn and Pasini have already shown that if n ≥ 4 and the line size is greater than or equal to four then the hyperplane complement ∆ − H is simply connected. Shpectorov proved a similar result for n ≥ 3 and line size five and above. We will prove a similar result for n ≥ 5 and line size three and above. We also...
متن کاملΠ Generalized Semi Connectedness in Intuitionistic Fuzzy Topological Spaces
The purpose o f this paper i s to introduce and study the concepts of intuitionistic fuzzy π generalized s e m i c o n n e c t e d n e s s in intuitionistic fuzzy topological space. Some of their properties are explored.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2022
ISSN: ['1435-9855', '1435-9863']
DOI: https://doi.org/10.4171/jems/1166