One point compactification for generalized quotient spaces

Metrization of the One-point Compactification

A new, more widely applicable, constructive definition of locally compact metric space is given, and a metric one-point compactification is constructed. Classically, this provides a simpler, more direct, construction of a metric on the one-point compactification of a separable locally compact metric

Nagata Compactification for Algebraic Spaces

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes. To the memory of Masayoshi Nagata

A Fixed Point Theorem in Generalized D-metric Spaces

Quotient cohomology for tiling spaces

We define a relative version of tiling cohomology for the purpose of comparing the topology of tiling dynamical systems when one is a factor of the other. We illustrate this with examples, and outline a method for computing the cohomology of tiling spaces of finite type.

Some Fixed Point Theorems for Generalized Contractions in Metric Spaces with a Graph

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...