Let C(f), Q(f), E(f) and A(f) be the sets of all continuity, quasicontinuity, upper and lower quasicontinuity and cliquishness points of a real function f: X → ℝ, respectively. The triplets (C(f),Q(f),A(f)), (C(f),E(f),A(f) and (Q(f),E(f),A(f)are characterized for functions defined on Baire metric spaces without isolated points.
Mappings preserving Cauchy sequences and certain types of convergences connected with these mappings are investigated.
A function is said to be almost quasicontinuous at if for each neighbourhood of . Some properties of these functions are investigated.
It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .
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