In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

In a study of surface branched coverings, one can ask naturally: In how many different ways can a given surface be a branched covering of another given surface? This problem was studied by many authors in Quart. J. Math. Oxford Ser. 2 46 (1995) 485, Math. Scand. 84 (1999) 23, Discrete Math. 156 (1996) 141, Discrete Math. 183 (1998) 193, Discrete Math. (in press), European J. Combin. 22 (2001) 1...

This paper provides the definitions of co-basis and co-covering graph. Using these new notations, it deals with the relationship between concept lattices and co-covering graphs. Afterwards, it solves the relation between complete lattices and co-covering graphs, and further, obtains that for a complete lattice, there is a concept lattice isomorphic to it. Mathematics Subject Classification: 06A...

Solar power development over canals is an emerging response to the energy–water–food nexus that can result in multiple benefits for water and energy infrastructure. Case studies of over-canal solar photovoltaic arrays have demonstrated enhanced performance due cooler microclimate next canal. In addition, shade from panels has been shown mitigate evaporation potentially aquatic weed growth. Howe...

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

Article history: Received 2 February 2011 Received in revised form 20 July 2011 Accepted 12 December 2011 Available online 19 December 2011

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...