Topological groups and covering dimension

Topological Games and Covering Dimension

We consider a natural way of extending the Lebesgue covering dimension to various classes of infinite dimensional separable metric spaces. All spaces in this paper are assumed to be separable metric spaces. Infinite games can be used in a natural way to define ordinal valued functions on the class of separable metric spaces. One of our examples of such an ordinal function coincides in any finit...

Covering Groups of Non-connected Topological Groups Revisited

All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let p : X̃ → X be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in X̃ with pẽ = e there is a unique structure of topological group on X̃ such that ẽ is th...

Generalized Covering Groups and Direct Limits

The topological ordering of covering nodes

The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

L-FUZZIFYING TOPOLOGICAL GROUPS

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...