The Wallman compactification is an epireflection

T(α, β)-spaces and the Wallman compactification

Wallman-type Compactifications

All spaces in this paper are Tychonoff. A Wallman base on a space X is a normal separating ring of closed subsets of X (see Steiner, Duke Math. J. 35 (1968), 269-276). Let T be a compact space and £ a Wallman base on T. For XCZT, define £x = {Ar)X\AE£}. Theorem 1. If X is a dense subspace of T, then T = w£x iff cItAHclrB = 0 whenever A, S£& and AC\B = 0. Theorem 2. T = w£xfor each dense XCZT if...

On Certain Wallman Spaces

Several generalized Wallman type spaces are considered as well as various lattices of subsets therein. In particular, regularity of these lattices and consequences are investigated. Also considered are necessary and sufficient conditions for these lattices to be Lindel6f as well as replete, prime complete, and fully replete.

Joshua Wallman 1943–2012

Josh Wallman was many things – a neuroscientist, an ornithologist, a teacher, a mentor, a gourmet, a joker. He pioneered the use of the avian model for understanding eye growth, and made invaluable contributions to vision research and the field of myopia. He will be remembered for his promotion of young researchers, his scientific acumen, and also his wit, which never faltered. Josh succumbed t...

An Alternative to Compactification

Conventional wisdom states that Newton’s force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gra...