By proving that, if the quotient space Σ(X) of the connected components of the locally compact metric space (X, d) is compact, then the full group I(X, d) of isometries of X is closed in C(X, X) with respect to the pointwise convergence topology, i.e., that I(X, d) coincides in this case with its Ellis’ semigroup, we complete the proof of the following: Theorem (a): If Σ(X) is not compact, I(X,...

Given a nonempty set X, a fuzzy ideal I on X is a collection of subsets of X closed under finite union and subset operations. In this paper we define a space to be locally I fuzzy compact space if every point in the space has an I fuzzy compact neighbourhood. Basic results concerning locally I fuzzy compact spaces are given relating to subspaces, preservation of functions, and products. Classic...

We give a short proof that the space of continuous functions from [0, 1] to [0, 1] is not compact in the compact-open topology. Suppose X and Y are compact topological spaces. Let C(X, Y ) be the space of continuous functions from X to Y , and give this space the compact-open topology. An interesting problem from topology is to prove or disprove that C(X, Y ) is compact. http://dx.doi.org/10.41...

in this paper the critical strain energy release rate for t300/913 carbon-epoxy laminated composites has been studied using ansys finite element software based on virtual crack closure technique ( vcct ). compact tension ( ct ) specimen has been used for numerical analyses and the geometrical dimensions have been extracted from the existing references. the results obtained from the finite eleme...

The known theory for an oid T shows how to find a subset T of ?T, which is a compact right topological semigroup [I]. The success of the methods in [2] for obtaining properties of-T has prompted us to see how successful they would be in another context. Thus we find (Theorem 4.8) that T cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger resu...