On the ΄΄Fragmentation΄΄ of Certain Pseydocompact Groups
A theorem of Stone-Čech type, and a theorem of Tychonoff type, without the axiom of choice; and their realcompact analogues
Functions linearly continuous on a product of Baire spaces.
Compact-covering numbers
Imposing psendocompact group topologies on Abeliau groups
The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, . We show: Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m, or α > ω and , then G admits a pseudocompact group topology of weight α. Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies . Theorem 5.2(b). If G is divisible Abelian with , then G admits at most -many...
Extending continuous functions on X x Y to subsets of βX x βY
Topologies induced by groups of characters
Some topological properties associated with measurable cardinals
On families of large oscillation
Extremal phenomena in certain classes of totally bounded groups
For various pairs of topological properties such that P ⇒ Q, we consider two questions: (A) Does every topological group topology with P extend properly to a topological group topology with Q, and (B) must a topological group with P have a proper dense subgroup with Q? We obtain negative results and positive results. Principal among the latter is the statement that any pseudocompact group G of uncountable weight which satisfies any of the following three conditions has both a strictly finer pseudocompact...
Cardinal invariants for κ-box products: weight, density character and Suslin number
The symbol (with κ ≥ ω) denotes the space with the κ-box topology; this has as base all sets of the form with open in and with . The symbols w, d and S denote respectively the weight, density character and Suslin number. Generalizing familiar classical results, the authors show inter alia: Theorem 3.1.10(b). If κ ≤ α⁺, |I| = α and each contains the discrete space 0,1 and satisfies , then . Theorem 4.3.2. If and with D(α) discrete, |D(α)| = α, then . Corollaries 5.2.32(a) and...
Locally compact realcompactifications
Some recent applications of ultrafilters to topology
Correction to the paper “The Bohr compactification, modulo a metrizable subgroup” (Fund. Math. 143 (1993), 119–136)
The Bohr compactification, modulo a metrizable subgroup
The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can hold for suitable...
Spaces Y Homeomorphic to ßY Y.
Continuous functions on products with strong topologies
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