Search results for "Second-countable space"

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The fractal interpolation for countable systems of data

2003

In this paper we will extend the fractal interpolation from the finite case to the case of countable sets of data. The main result is that, given an countable system of data in [a, b] ? Y, where [a, b] is a real interval and Y a compact and arcwise connected metric space, there exists a countable iterated function system whose attractor is the graph of a fractal interpolation function.

Discrete mathematicsMetric spaceFractalIterated function systemGeneral MathematicsAttractorMathematics::General TopologyCountable setSecond-countable spaceCosmic spaceInterpolationMathematicsPublikacije Elektrotehnickog fakulteta - serija: matematika
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Countable connected spaces and bunches of arcs in R3

2006

Abstract We investigate the images (also called quotients) of countable connected bunches of arcs in R 3 , obtained by shrinking the arcs to points (see Section 2 for definitions of new terms). First, we give an intrinsic description of such images among T 1 -spaces: they are precisely countable and weakly first countable spaces. Moreover, an image is first countable if and only if it can be represented as a quotient of another bunch with its projection hereditarily quotient (Theorem 2.7). Applying this result we see, for instance, that two classical countable connected T 2 -spaces—the Bing space [R.H. Bing, A connected countable Hausdorff space, Proc. Amer. Math. Soc. 4 (1953) 474], and th…

Discrete mathematicsTopological manifoldWeakly first countable spacesFirst-countable spaceMathematics::General TopologySecond-countable spaceCountable connected spacesBaire spaceCosmic spaceSeparable spaceCombinatoricsMathematics::LogicMetric spaceCountable setBunches of arcsGeometry and TopologyMathematicsTopology and its Applications
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