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Compactifications of ℕ and Polishable subgroups of S ∞

Todor Tsankov (2006)

Fundamenta Mathematicae

We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group S ∞ . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of S ∞ . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ a certain Polishable...

Compatible mappings of type (B) and common fixed point theorems in Saks spaces

H. K. Pathak, M. S. Khan (1999)

Czechoslovak Mathematical Journal

In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.

Compatible mappings of type ( β ) and weak compatibility in fuzzy metric spaces

Shobha Jain, Shishir Jain, Lal Bahadur Jain (2009)

Mathematica Bohemica

The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type ( β ) and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics ( 2006 ) ] and Sharma [Fuzzy Sets and Systems ( 2002 ) ] . An example has been constructed in support of our main result. All the results presented in this paper are new.

Complete ℵ 0 -bounded groups need not be ℝ -factorizable

Mihail G. Tkachenko (2001)

Commentationes Mathematicae Universitatis Carolinae

We present an example of a complete ℵ 0 -bounded topological group H which is not ℝ -factorizable. In addition, every G δ -set in the group H is open, but H is not Lindelöf.

Complete pairs of coanalytic sets

Jean Saint Raymond (2007)

Fundamenta Mathematicae

Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of ω ω there exists a continuous function f : ω ω → X such that f - 1 ( C ₀ ) = D ₀ and f - 1 ( C ₁ ) = D ₁ . We give several explicit examples of complete pairs of coanalytic sets.

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