the results, we proposed a partial generalization of Shelah's Theorem to higher homotopy groups for noncompact spaces. Also, we discuss n-homotopically Hausdorff property, a separation axiom for n-loops introduced in [12], and conclude that each subset of Rn+1...

In this paper, n-homotopically Hausdorff and strongly n-homotopically

Hausdorff spaces are introduced. It is proved that every subset of 3-dimensional

Euclidean space is 2-homotopically Hausdorff, and that every strongly nhomotopically...

In this paper, we provide a nerve theorem for locally wellbehaved

spaces and apply it to provide a generalization of Shella’ Theorem

to higher homotopy groups for compact and noncompact spaces.

Also, we discuss n-homotopically...

This paper is devoted to spaces that are not homotopically Hausdorff and study their covering spaces. We introduce the notion of small covering and prove that every small covering of $X$ is the universal covering in the categorical sense. Also, we...

H. Fischer et al. (Topology and its Application, 158 (2011) 397-408.) introduced the Spanier group of a based space $(X,x)$ which is denoted by $\\psp$.

By a Spanier space we mean a space $X$ such that $\\psp=\\pi_1(X,x)$, ...

group when $X$ is $H$-SLT space at $x_0$ and $H$ is a normal subgroup. Also, we show that under these conditions the concepts of homotopically path Hausdorff relative to $H$ and homotopically Hausdorff relative to $H$ coincide. Moreover, among other...