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Almost closed sets and topologies they determine

Vladimir Vladimirovich Tkachuk, Ivan V. Yashchenko (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove that every countably compact AP-space is Fréchet-Urysohn. It is also established that if X is a paracompact space and C p ( X ) is AP, then X is a Hurewicz space. We show that every scattered space is WAP and give an example of a hereditarily WAP-space which is not an AP-space.

Almost disjoint families and “never” cardinal invariants

Charles Morgan, Samuel Gomes da Silva (2009)

Commentationes Mathematicae Universitatis Carolinae

We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to ω 1 under the effective weak diamond principle ( ω , ω , < ) , answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property ( a ) in spaces from almost disjoint families,...

Almost g ˜ α -closed functions and separation axioms

O. Ravi, S. Ganesan, R. Latha (2012)

Mathematica Bohemica

We introduce a new class of functions called almost g ˜ α -closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost g ˜ α -closed continuous surjections.

Almost maximal topologies on groups

Yevhen Zelenyuk (2016)

Fundamenta Mathematicae

Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...

Almost * realcompactness

John J. Schommer, Mary Anne Swardson (2001)

Commentationes Mathematicae Universitatis Carolinae

We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness.

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