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Bornological quasi-metrizability in generalized topology

Artur PİĘKOSZ [1] , Eliza WAJCH [2]

A concept of quasi-metrizability with respect to a bornology of a generalized topological space in the sense of Delfs and Knebusch is introduced. Quasi-metrization theorems for generalized bornological universes are deduced. A uniform quasi-metrizability with respect to a bornology is studied. The class of locally small spaces is considered and a possibly larger class of weakly locally small spaces is defined. The proofs and numerous examples are given in ZF. An example of a weakly locally small space which is not locally small is constructed under ZF+CC. Several categories, relevant to generalized bornological universes, are defined and shown to be topological constructs.
Delfs-Knebusch generalized topological space, quasi-metric, bornology, topological category, ZF
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-7515-2418Author: Artur PİĘKOSZ (Primary Author)Institution: Cracow University of TechnologyCountry: Poland Orcid: 0000-0003-1864-2303Author: Eliza WAJCH Institution: Siedlce University of Natural Sciences and HumanitiesCountry: Poland Publication Date : December 8, 2019
 Bibtex @research article { hujms656663, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1653 - 1666}, doi = {}, title = {Bornological quasi-metrizability in generalized topology}, key = {cite}, author = {PİĘKOSZ, Artur and WAJCH, Eliza} } APA PİĘKOSZ, A , WAJCH, E . (2019). Bornological quasi-metrizability in generalized topology. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1653-1666 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/50516/656663 MLA PİĘKOSZ, A , WAJCH, E . "Bornological quasi-metrizability in generalized topology". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1653-1666 Chicago PİĘKOSZ, A , WAJCH, E . "Bornological quasi-metrizability in generalized topology". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1653-1666 RIS TY - JOUR T1 - Bornological quasi-metrizability in generalized topology AU - Artur PİĘKOSZ , Eliza WAJCH Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1653 EP - 1666 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Bornological quasi-metrizability in generalized topology %A Artur PİĘKOSZ , Eliza WAJCH %T Bornological quasi-metrizability in generalized topology %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R %U ISNAD PİĘKOSZ, Artur , WAJCH, Eliza . "Bornological quasi-metrizability in generalized topology". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1653-1666 . AMA PİĘKOSZ A , WAJCH E . Bornological quasi-metrizability in generalized topology. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1653-1666. Vancouver PİĘKOSZ A , WAJCH E . Bornological quasi-metrizability in generalized topology. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1666-1653.