Some applications of tiny sequences
Products and measurable cardinals
Category bases.
Remarks on the absolute suspension
Undecidability of the existence of regular extremally disconnected S-spaces
On spaces with binary normal subbase
On -caliber and an application of Prikry’s partial order
We study the concept of -caliber as an alternative to the well known concept of caliber. -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, is a -caliber of . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.
Measurable cardinals and category bases
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
Some Baire category type theorems for
Subbase characterization of special spaces
Short proofs of two theorems in topology
We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A weakly -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.
On Nash theorem
Theorem on signatures
Absolute points in
Compatibility and statistical inference for data in measurement model of Foulis and Randall
Eberlein spaces of finite metrizability number
Yakovlev [, Comment. Math. Univ. Carolin. (1980), 263–283] showed that any Eberlein compactum is hereditarily -metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.
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