We discuss instantons in dimensions higher than four. A generalized self-dual or anti-self-dual instanton equation in n-dimensions can be defined in terms of a closed (n − 4) form Ω and it was recently employed as a topological gauge fixing condition in higher dimensional generalizations of cohomological Yang-Mills theory. When Ω is a calibration which is naturally introduced on the manifold of...

Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group F (X) over a Tychonov space X is o-bounded if and only if every continuous metrizable image T of X satisfies the selection principle S fin(O,Ω) (the latter means that for every sequence 〈un〉n∈ω of open covers of T there exists a sequence 〈vn〉n∈ω such that vn ∈ [un] and for every F ∈ [X] ther...

We discuss instantons in dimensions higher than four. A generalized self-dual or anti-self-dual instanton equation in n-dimensions can be defined in terms of a closed (n − 4) form Ω and it was recently employed as a topological gauge fixing condition in higher dimensional generalizations of cohomological Yang-Mills theory. When Ω is a calibration which is naturally introduced on the manifold of...

Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C0(Ω) ′′ of the C∗-algebra C0(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω. We shall study the C∗-algeb...

In this paper, we introduce Tαm-Super-Spaces, αm-contra-closed maps, αm-contra-open αm-contra-continuous αm-contrairresolute b-ω-open sets and Continuity via studied some of their properties

Cardinal invariants related to sequential separability of generalized Cantor cubes 2κ, introduced by M. Matveev, are studied here. In particular, it is shown that the following assertions are relatively consistent with ZFC: (1) 2ω1 is sequentially separable, yet there is a countable dense subset of 2ω1 containing no non-trivial convergent subsequence, (2) 2ω1 is not sequentially separable, yet ...