We will show that every KC-function f : X×Y → Z is strongly quasi-continuous provided that X is Baire,

Y a W-space and Z is regular. It follows that if Y is a Moore W-space and G is a Baire left topological

group, ...

In this talk, after reviewing concepts of compact-open topology, Whisker topology

and Lasso toplogy on fundamental groups, we present some topological properties for

the Whisker topology on a fundamental group.

_n(Y_i^{(n)},y_i^*)} is bijection. Second, using this fact we prove that

the topological n -homotopy group of an n -Hawaiian like space, pi_n^{top}(X,x^*), is a

topological group for all n geq 2 which is a partial answer to the open question whether

pi...

spaces, which make them Hausdorff topological groups. We then exhibit an example in which $\\check{\\pi}_k^{top}$ succeeds in distinguishing the shape type of $X$ and $Y$ while $\\check{\\pi}_k$ fails, for all $k\\in \\Bbb{N}$. Moreover, we present some...

We continue our work (Jabbari and Vishki in Bull. Aust. Math. Soc. 79:

129–145, 2009) to give a more explicit characterization of the topological centre of

the Ellis groups corresponding to the so-called skew ...

^*(X,Y)$, for arbitrary topological spaces $X$ and

$Y$. In particular, we can consider a topology on the coarse shape homotopy group of a topological space $(X,x)$, $Sh^*((S^k,*),(X,x))=\\check{\\pi}_k^{*}(X,x)$, which makes it a Hausdorff topological group...

})$, respectively. In particular, we give necessary or sufficient conditions for equality and being topological group of these two topologized fundamental groups. Finally, we give some examples to show that the converse of some of these implications do not hold...

Following [1] and [5], if Gis a finite group, the probability

that two randomly chosen elements of Gcommute is defined to becom(G)/|G|^2, where com(G) is the number of pairs

(x,y)in G times G$ with xy=yx For ...

The topological centre of the Ellis group of a class of distal flows arised from some function is studid.

Equivariant functions can be useful for constructing of maximal invariant statistic. In

this article, we discuss construction of maximal invariants based on a given weakly

equivariant function under some ...