A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X , if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X . A locally connected space is straight iff it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the ...

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Hor...

‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

A detailed structure theorem is shown for locally compact, locally connected, hereditarily normal spaces and for normal, locally compact, locally connected, hereditarily ω1-scwH spaces in models of PFA(S)[S], and for the latter kinds of spaces in models of PFA. Corollaries include a powerful refinement theorem like that for monotonically normal spaces, and the corollary that the spaces involved...

We investigate the question which (separable metrizable) spaces have a ‘large’ almost disjoint family of connected (and locally connected) sets. Every compact space of dimension at least 2 as well as all compact spaces containing an ‘uncountable star’ have such a family. Our results show that the situation for 1-dimensional compacta is unclear.  2004 Elsevier B.V. All rights reserved.

1 Topological Spaces 1 1.1 Continuity and Topological Spaces . . . . . . . . . . . . . . . 1 1.2 Topological Spaces . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Metric Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.4 Further Examples of Topological Spaces . . . . . . . . . . . . 3 1.5 Closed Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.6 Hausdorff ...

0.1. Why Do We Want to Decompose a Space? Basically the goal of mathematics is to classify certain objects. For instance, we are able to classify 2-dimensional manifolds. Then we are trying to classify 3-manifolds while Poincaré conjecture sounds difficult to be solved. In homotopy theory, a general question is how to classify spaces (up to homotopy). The general idea for classifying spaces is:...