Kekontinuan Fungsi Pada Ruang Metrik

Pengertian fungsi di kalkulus adalah pemetaan dari himpunan bilangan real ke himpunan bilangan real dengan fungsi jaraknya adalah nilai mutlak. Pada makalah ini akan disajikan pengertian fungsi dari suatu ruang metrik ke ruang metrik yang lain yang fungsi jaraknya mungkin saja berbeda. Selanjutnya akan dibicarakan mengenai limit fungsi pada ruang metrik, kekontinuan fungsi pada ruang metrik, fungsi kontinu seragam pada ruang metrik, kekompakan fungsi pada ruang metrik, dan teorema-teorema yang berhubungan dengan hal tersebut. Kata Kunci : Ruang Metrik, Limit Fungsi, Fungsi Kontinu, Fungsi Kompak. Notion of a function in calculus is a mapping from the set of real numbers to the set of real numbers with absolute value it is. On this paper will be presented the notion of functions of a metric space into the other metric space with the functions of the distance is probably different. Next will be discussed regarding the limit of a function on a metric space, the continuous function on metric spaces, uniform continuity on the space metric, a metric space compactness function and theorems that relates to it. Key words : Metric Space, Limit Of The Function, The Continuous Function, Compact Function

Topics in uniform continuity

This paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizing Atsuji spaces) where all continuous functions have the property of being close to uniformly continuous

Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)

We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both topological and algebraical senses. Corresponding results are also obtained concerning unbounded continuous functions on a non-compact metrizable space.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ