Wallman Compactification in FTS

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...

Induced Measures on Wallman Spaces

Let X be an abstract set and .t; a lattice of subsets ofX. To each lattice-regular measure we associate two induced measures and on suitable lattices of the Wallman space Is(L) and another measure IX’ on the space I,(L). We will investigate the reflection of smoothness properties of IX onto t, and Ix’ and try to set some new criterion for repleteness and measure repleteness.